How can I achieve the same flavor and texture as roasted garlic without an oven?

I have had great results by taking individual garlic cloves and cutting the root end off each, but leaving them in their papery skins.

Then you put those dry into a small saucepan (ideally one with a thick bottom) over low-to-medium heat. Put a lid on it, and let it go for 20 minutes or so, shaking vigorously every couple of minutes to turn the cloves over. When the cloves are really soft, you're done.

The paper skins protect the garlic cloves from burning, but the direct contact with the hot pan cooks them nicely. When you're done you can squeeze the soft, roasted garlic goodness out of the root end of the skins. This is a particularly nice technique when you want roasted garlic flavor but only need a few cloves, not a whole head.

The first time I did a recipe that called for this process, I was sure the garlic would scorch or the skins would catch fire, but it worked great.

You can get the same result by frying the garlic in a saucepan of oil.

Place peeled cloves in a saucepan and add enough light olive oil or canola oil to just cover the cloves. Cook at medium to medium-low heat, stirring not too often until the garlic becomes golden brown.

Strain the cloves into a strainer or colander to remove excess oil, but save as much of the oil as you can. It is now filled with the lovely roasted garlic flavor, and is wonderful for sauces, salad dressings, and drizzling over cooked foods.

If you don't mind a less-neutral base oil, you can use good extra-virgin olive oil instead of light olive oil. The resulting infused oil will have an even richer flavor.

My first suggestion would be a "dutch oven" at a low temperature. If you have a small ceramic dish you might set that into the dutch oven and then the garlic into the dish in order to further manage the "low and slow" effect that is desired for roasting garlic. (add a couple of small wood chips on some aluminum foil in the pot but away from the garlic to create a 'smoked garlic'...if you like that.)

If you can invest in additional kitchen equipment, you might consider a small crock pot to get the same results.

Roasted garlic needs a lot of slow, even heat to cook through and not burn. I doubt that you will be able to replicate this without an oven or oil. I have two ideas that might work.

First, take four or five heads of garlic and cut them flat at the stem and place a little bit of oil in a pan to sear the cut surface until it begins to caramelize mostly to get the process started and begin to develop the roasted flavor. Then place the head of garlic up so it sits on its side in a crock pot. I bet in four or five hours it would make nice roasted garlic. (I've never done this but would like to try.)

I know a very famous French Chef who boils the garlic for his vichyssoise in milk for about half and hour to take out the bitter, spicy bite. So if you need soft, sweet garlic for pureeing to use instead of roasted you can boil it in milk first. Because if you saute the garlic raw it might burn before the inside is softened, boiling before using a little oil in a pan to saute the garlic to get some complicated flavor and color might work very well.

These are just two alternatives to the other answer of cooking the garlic in oil. However, it is very frequent that restaurants will cook the garlic in oil to not only get nice caramelized garlic but also amazing flavored oil to use as a condiment or in salad dressings.

You might want to look up confit garlic.

Hot air rises and one needs a vegetable steamer, or crumpled aluminum foil will do, for the bottom of the pan, or both, to keep the garlic from burning on the bottom. The drizzled evo over the tops of the garlic cloves is important and keeps garlic moist. A cast iron skillet and lid, plus the mechanism to keep the garlic off of the bottom, works beautifully.

My technique is to heat the iron skillet, put in the steamer amd foil, and wrapped garlic on top, and immediately turn the flame down to low. The fragrance of the garlic will surely alert the chef when the garlic is ready, or almost roasted. Doubtful you will have a 'burned head of garlic, if you check after 25 - 35 minutes, then roast longer if necessary. Also, I have used an oven thermometer sitting in the pot on top of the vegetable steamer and foil to help regulate the heat. This method is better for me, because it uses less energy than heating an entire oven for one head of roasted garlic.