Preheat oven to 450° with rack on bottom. Wearing long gloves, rinse nettles well. Drain.
Sizzle garlic a few seconds in 1 tbsp. oil in a large frying pan over medium-high heat. Add nettles and sauté until wilted, 2 to 5 minutes. Remove from heat. If nettles are wet, drain in a colander, pat dry, and return to pan. Gently mix nettles with 1 tbsp. more oil, the pepper, and chile flakes.
Roll dough on a floured board into a 9- by 14-in. rectangle. Ease dough onto an oiled baking sheet, fixing the shape if necessary. Using fingers, roll edges of dough over to make a 1/2-in. rim.
Scatter cheese, then nettles, over dough. Bake until crust is crisp, 15 minutes. Drizzle with remaining 1 tbsp. oil and cut into squares. Season with salt if you like.