Heat the oven to 425°F with a large, rimmed sheet pan inside it. A preheated pan starts browning the moment the potatoes land, which is free crispness.
Cut the potatoes into even 1 1/2-inch wedges or chunks. Halve small potatoes, quarter medium ones, and cut large ones into 6 to 8 pieces. Even size matters more than exact shape, since uneven pieces cook unevenly.
Rinse the cut potatoes briefly under cold water, then dry them thoroughly with a clean towel. Wet potatoes steam instead of roasting, and this drying step is the single biggest difference between crisp and soggy results.
Toss the dry potatoes with the olive oil, kosher salt, and pepper in a large bowl until every piece glistens. Carefully spread them on the hot pan in a single layer, cut-side down where possible, with gaps between pieces. Do not crowd the pan; use a second pan if you must.
Roast for 20 minutes without touching them, so a crust forms on the pan side. Flip each piece with a metal spatula, then roast 12 to 15 minutes more. In the last 5 minutes, scatter the sliced garlic and rosemary over the pan and roast until the garlic is pale gold and the potatoes are deeply golden and fork-tender.
Taste, adjust salt, and shower with flaky salt and parsley if you like. Serve hot, straight from the pan, since crispness fades as the potatoes sit.