- Make the pesto: Combine all ingredients in a food processor. Pulse until completely combined, scraping sides as necessary. Refrigerate for up to 1 week. (This recipe makes extra, because it’s good on everything.)
- Make the galette: Whisk egg with 1 tablespoon water to make an egg wash; set aside. On a lightly floured surface, roll out dough into a circle about 10 inches in diameter. Place on a parchment-lined sheet tray. Spread a layer of pesto onto dough, leaving a 1-inch border. Slice tomatoes very thin, and place on top of pesto, slightly overlapping, forming a ring. Fold dough at edges to make a border and brush with egg wash. Sprinkle chopped sunflower seeds, sea salt, and black pepper over edge of the tart. Chill until ready to bake.
- Bake at 400 degrees for 35 to 40 minutes, rotating halfway through baking. The tart is done when it is golden brown and puffed. Let cool slightly before serving.