Alternative to potatoes

If you want a similar texture and flavor, I recommend trying other similar root vegetables.

I use turnips and parsnips in similar applications. They're both dense, white and have a slight sweetness to them and they should hold up relatively well to long cooking times.

You might also enjoy yucca which can have a cooked texture similar to a cross between potato and banana. I've not tried them in this sort of application specifically but I think they should work.

Apart from "other root vegetables", unripe plantains and hard squash are starchy and substantial like potatoes are, and can be used; for optimal results, the cooking method might need to be adapted. Plantains will be best sauteed or fried before being added. With hard squash one needs to take care not to overcook it, so adding it later in a long-stewing dish might be advantageous.

In some cases, hard fruit (apples, heirloom pears, pineapple etc.) can also work, but will obviously change the result significantly.

Try chayote, it's a great substitute for any starch. It's got a nice crisp to it raw, cooks down to a nice texture, and doesn't really have any taste of its own.¹ It takes on the flavors of whatever it cooks with; some even use it as a substitute for apples in desserts after flavoring it because it holds up extremely well (think of those deep fried pies you can get at fast food places).

Roasting along with carrots and other vegetables in a stock would leave it with a very nice taste; it won't alter the flavor or outcome of the dish. I frequently use it in soups because getting a piece of it in a bite really amplifies the taste of the stock. It's also rich in vitamin C.

The drawback is that it doesn't break down as easily as potatoes do while roasting, and won't have that sort of mild thickening / fortifying effect. But you could easily work around that.

Alternatively, parsnips (as others suggested) if you can't find chayote, but parsnips and other roots bring a new flavor to the table.

¹_{If you have a very sensitive palate, you will detect a very mild flavor, but it's very easily overpowered by practically anything.}