Preheat oven to 425°. Lay out a sheet of parchment paper, unroll pie dough on top, and roll into a 13-in. round. Set on a rimless baking sheet.
Leaving a 2-in. border, scatter cheese, chorizo, potatoes, and peppers over dough.
Fold dough edges over filling, then bake until crust is golden and cheese is melted, 20 to 25 minutes.
Toss arugula with vinegar and oil in a small bowl until coated. Scatter over galette. Cut into wedges and serve immediately.
*We especially like Pillsbury pie dough. Look for Barinaga Ranch Baserri, a California farmstead cheese sold at specialty shops, or use manchego.
Note: Nutritional analysis is per serving.