Prepare the pastry: Add flour and salt to a food processor and pulse twice. Add butter and pulse until crumbly, leaving some large pieces of butter. Drizzle ice water and vinegar over the mixture and pulse again until the dough starts to come together. Turn the dough out onto a clean surface. Knead very lightly until everything comes together—do NOT overwork. Form the dough into a disk and wrap it in plastic wrap. Refrigerate for at least 1 hour and up to 2 days.

Preheat oven to 400 degrees F. Line a sheet pan with parchment paper.

Prepare the filling: Heat olive oil in a large skillet over medium heat. Add onion, season with salt and pepper, and sauté for 5–7 minutes, stirring often. Push onions to the edges and add carrots in a single layer, season again, and cook for about 5 minutes, flipping once. Stir in greens and garlic, season again, and cook for 3–5 more minutes, until greens wilt and turn bright green. Remove from heat and set aside. Place ricotta, goat cheese, one egg, ½ tablespoon parsley, and a pinch of black pepper in a medium bowl and whisk until smooth.

Make the galette: On a lightly floured surface, roll the dough into a large oval, about ¼ inch thick and about the size of a half-sheet pan. Rotate it occasionally as you roll to prevent the bottom from sticking. Gently transfer the dough to the parchment-lined pan (to transfer, roll it around a floured rolling pin and unroll it onto the paper). Spread cheese mixture over the pastry leaving a 2-inch margin around the edges. Mound the vegetables over the cheese. Fold the edges over the filling, making pleats as you go. Brush the beaten egg over the edges of the pastry. Bake for 40–45 minutes, until golden brown. Let cool for about 10 minutes. Sprinkle with remaining ½ tablespoon parsley and cut into wedges.