How to Make It
Preheat oven to 400°F. Lightly coat an 8-inch round cake pan with cooking spray. Heat 1 tablespoon oil in a large nonstick skillet over medium-high. Add sprouts, cut sides down; cook, stirring occasionally, until beginning to brown, about 5 minutes. Add 1/4 cup water; reduce heat to medium. Cover and cook, undisturbed, until sprouts are tender when pierced with tip of a knife, about 4 minutes. Transfer to prepared cake pan; arrange evenly, cut sides down.
Wipe skillet clean. Add remaining 1 tablespoon oil; heat over medium-low. Add shallot; cook, stirring often, until softened, 3 to 4 minutes. Stir in vinegar, honey, thyme, salt, and pepper; cook, stirring constantly, until liquid is slightly syrupy, about 2 minutes. Drizzle evenly over sprouts. Drape pie dough over sprouts, tucking edges into sides of cake pan. Prick top all over with a fork or tip of a knife.
Bake at 400°F until crust is golden brown, 25 to 30 minutes. Transfer to a wire rack to cool 5 minutes. Carefully invert onto a serving plate.