Preheat oven to 400°. Lightly dust a work surface with flour. Roll out pie crust into a 10- by 13-in. rectangle (if using a rectangular tart pan) or an 11-in. round (if using a round tart pan). Carefully transfer crust to an 8- by 11-in. tart pan or a 9-in. round tart pan with a removable rim, pressing dough into corners and folding it back inside edges of pan if needed so it’s flush with top of pan. Crumple a piece of parchment paper that’s big enough to come a couple inches above sides of tart and lay in crust. Fill with pie weights or dried beans.
Place tart pan on a rimmed baking sheet and bake until golden brown at edges, about 15 minutes. Lift out parchment and pie weights but leave tart pan on baking sheet.
Meanwhile, heat a small frying pan over medium heat. Add pancetta and cook until very crisp, 8 to 15 minutes. With a slotted spoon, transfer pancetta to paper towels.
Whisk eggs in a large bowl to blend. Stir in asparagus, 1 tbsp. chives, the crème fraîche, salt, and pepper until fairly well blended. Fold in pancetta. Pour filling into warm crust and dot with goat cheese.
Bake until filling is set in center when tart is gently shaken, 13 to 20 minutes. Let tart cool on a rack about 10 minutes. With a small knife, loosen crust from edge of pan. Carefully push tart out and set on a platter. Sprinkle with the remaining 1 tbsp. chives and cut into squares or wedges. Serve warm or at room temperature.