Onion Anchovy Galette

Blend together flour, butter, and salt in a bowl with your fingertips or a pastry blender (or pulse in a food processor) just until most of mixture resembles coarse meal with some roughly pea-size butter lumps.
Drizzle 3 tablespoons ice water evenly over mixture and gently stir with a fork (or pulse in processor) until incorporated.
Squeeze a small handful: If it doesn't hold together, add more ice water, 1/2 tablespoon at a time, stirring (or pulsing) until incorporated, then test again. (Do not overwork mixture or pastry will be tough.)
Turn out mixture onto a lightly floured surface and divide into 4 portions. With heel of your hand, smear each portion once or twice in a forward motion to help distribute fat. Gather dough together, with a pastry or bench scraper if you have one, and press into a ball, then flatten into a 5-inch disk. Chill, wrapped in plastic wrap, until firm, at least 1 hour.
Cook onions in oil and butter in a 12-inch heavy skillet over medium heat, stirring occasionally, until softened and golden, about 30 minutes.
Preheat oven to 375°F with rack in middle.
Finely chop anchovies and garlic together. Stir together with tomato paste and thyme.
Roll out dough on a lightly floured surface with a lightly floured rolling pin into a 13-inch round. Transfer to a parchment-lined large baking sheet.
Spread tomato-anchovy mixture over dough, leaving a 2-inch border along edge, then arrange onions on top. Fold edges of dough inward. Bake until pastry is golden, 45 to 50 minutes. Serve warm or at room temperature.