Broccolini and Feta Galette

In a medium bowl, combine flour, oil, 1 teaspoon salt, and 1/3 cup cold water. With a fork, stir to combine. Knead dough 1 minute. Cover with plastic wrap and let rest 30 minutes.

Preheat oven to 400 degrees, with rack in lower third. In a large pot of boiling salted water, cook Broccolini until bright green, 1 minute. With tongs, transfer to a paper-towel-lined plate.

Roll out dough to a 14-inch round; transfer to a parchment-lined baking sheet. Sprinkle dough with Parmesan and top with Broccolini, leaving a 2 1/2-inch border. Top with feta and red-pepper flakes; season with salt and pepper. Fold dough border over filling and brush with egg. Bake until crust is golden brown, 35 to 40 minutes. Serve warm or at room temperature.