You want to slice the radishes somewhat thick, but not too thick. The trick here is to get the potato and radish slices to be ready at the same time

4 c potatoes, quartered or thickly sliced
olive oil, for roasting vegetables plus 1 T extra for dressing
salt and pepper, to taste
2 c sliced or chunked (peeled) radishes
3 – 4 T Greek-style yogurt or sour cream
1 T lemon juice
2 cloves garlic, finely minced, or mashed to a purée
fresh, chopped parsely or chives or other herb, or dried version

1. Preheat oven to 425°F. Toss potatoes with olive oil, salt, and pepper. Transfer to a baking sheet and spread out in a single layer. Roast for about 10 minutes, then flip the potatoes or stir them about. Return to oven and roast for another 10 minutes.

2. Meanwhile, toss the sliced radishes with olive oil, salt, and pepper. When the potatoes have roasted for 20 minutes total, remove baking sheet from oven. Stir potatoes and move them to one side or around the perimeter of the baking sheet. Place the radishes in the space vacated by the potatoes. Return to oven and roast for another 20 minutes, stirring at least once, until the potatoes and radishes are browned and crispy (but not burnt) on the outside.

3. Remove from oven and transfer to a serving bowl. Let cool some while you prepare the dressing. Combine the yogurt or sour cream, 1 T olive oil, lemon juice, garlic, a bit of salt and pepper (remember you’ve already seasoned the vegetables before roasting), and herb, if using. Add dressing to potatoes and toss to combine. Taste for seasonings and serve.