Cheesy Loaded Sweet Potatoes

3 lb. sweet potatoes (4 large or 6 small), scrubbed, halved lengthwise
3 Tbsp. extra-virgin olive oil, divided
1 1/2 tsp. kosher salt
1/2 tsp. freshly ground black pepper
1 1/2 cups shredded Monterey Jack or cheddar cheese
Sour cream or plain yogurt, sliced avocado, thinly sliced radishes, thinly sliced scallions, cilantro leaves, Pickled Red Onions, lime wedges, and/or hot sauce (for serving; optional)

Fill a large pot with 1" water. Place potatoes in a steamer basket and lower into pot. Cover pot and bring to a boil. Steam until potatoes are fork-tender, 25–30 minutes.
Place an oven rack about 8" from broiler; preheat broiler. Coat a rimmed baking sheet with 1 Tbsp. oil. Arrange potatoes skin side down on prepared pan. Score or lightly mash flesh with a fork; season all over with salt and pepper. Drizzle with remaining 2 Tbsp. oil, then top with cheese (taking care to keep it on the potatoes, not the pan). Broil potatoes, watching carefully to make sure they don’t burn, until cheese is bubbling and golden brown, 3–5 minutes.
Transfer potatoes to a platter. Serve with sour cream, avocado, radishes, scallions, cilantro, pickled onion, lime wedges, and hot sauce for topping alongside, if desired.
Do Ahead: Potatoes can be steamed 5 days ahead. Transfer to an airtight container and chill.