Is there a way to lessen the unpleasant smell of steamed broccoli?

Cook it less, if you can. The more you cook it, the more you get that smell. Perhaps you are just more sensitive to it than most; I don't generally notice it until it's overcooked by my standards.

Along with this, cook it as fast as you can. The flavor you don't like is produced by enzymes converting precursor molecules into those with the flavor. From On Food and Cooking:

Heating cabbages and their friends has two different effects. Initially the temperature rise...speeds the enzyme activity and flavor generation, with maximum activity around 140F/60C. The enzymes stop working altogether somewhere short of the boiling point. If the enzymes are quickly inactivated by plunging the vegetables into abundant boiling water, then many of the flavor precursor molecules will be left intact. ... If the cooking period is prolonged, then the constant heat gradually transforms the flavor molecules. Eventually the sulfur compounds end up forming trisulfides, which accumulate and are mainly responsible for the strong and lingering smell of overcooked cabbage.

So as suggested by others, boiling instead of steaming to reduce cooking time helps. So does cooling quickly, with cold or ice water. Boiling in excess water will also leach some out, but you might also lose flavor you like.

A couple other thoughts, also from On Food and Cooking. Cabbage family vegetables grown in the summer, and under drought stress, produce more of the flavor precursors, and those grown in the autumn and winter with less light and more water have less. They're also more concentrated in the core of the vegetables. And for cabbage, you can remove a lot of them by chopping and soaking in cold water; conceivably the same could work for broccoli, but again perhaps at the cost of desirable flavor.

This does not happen if you boil it for 30-60 seconds, drain, then ice water shock the broccoli instead of steaming.

In steaming, the usual way to prevent this is to eat it quickly and to steam for a very short time. However, steaming to the same point of moderate tenderness takes at least 6 minutes at high pressure, and the cooking doesn't stop after you remove it.

In my experience, blanching provides superior results for broccoli's flavor compared to steaming, even if you end up recooking the broccoli (like you might in a casserole), because the halting of the cooking process from the rapid cooling.

It's possible that ice water shocking steamed broccoli may have the same effect, but I prefer the shorter cooking time that blanching enables so I've never tried it. It may be worth experimenting with, if you're committed to steaming.

I've never had a problem, but I also don't do a 100% steam cooking method ... you may want to try it and see if it sets off your nose, as we're all sensitive to smells to a different degree:

1. Heat a skillet with a little bit of oil in it. (you can use non-stick, but you still want a little bit of oil)
2. Cut up the flourets, but set them aside.
3. Slice up the stem
4. Sauté the stems for a minute or two.
5. Add the flourets, and saute for another 30-60 seconds.
6. Add a bit of water, and slap on a lid.
7. Let steam to your desired doneness.
8. Drain off the water (tilt pan over sink while holding lid slightly askew)
9. Serve

I left out the seasoning step ... I typically season when sautéing, but if you're used to steaming, it might be more similar to season after cooking.

We love all things broccoli ; soup included. I always add a pinch of baking soda, and that's the end of the odour. Good luck.

I have always had good results with adding a stalk of celery when steaming broccoli, and then discarding it after cooking. Don't know why it works, but my mom had done this for years after reading it in some cookbook, and it does seem to change the odor that permeates the kitchen.