To prepare the galette rounds: In a bowl, whisk together milk, butter, yolks, and whole egg. In another bowl whisk together flour, salt, and chives and stir into milk mixture until just combined.
On a lightly floured surface with floured hands, knead dough about 8 times, or until just smooth. Wrap dough in plastic wrap and chill 1 hour.
Preheat oven to 450 degrees F.
Divide dough into 4 pieces, freeze 2 of them. On a lightly floured surface with a floured rolling pin roll out each piece into an 8-inch round. Transfer rounds to 2 baking sheets and crimp edges decoratively. Chill dough 10 minutes and bake in middle and lower thirds of oven about 5 minutes, or until golden brown. Transfer galettes to racks and cool completely. Galettes may be made 1 day ahead and kept in a sealable plastic bag at room temperature. Lower oven temperature to 400 degrees F.
In a bowl stir together olive paste and basil. In another bowl stir together ricotta, Parmesan, and salt and pepper, to taste. Spread olive mixture evenly onto galette rounds and spread cheese mixture over it. Cover cheese mixture with tomatoes and season with salt and pepper. Bake galettes on a baking sheet in middle of oven about 15 minutes. Transfer galettes to a rack and cool.
Serve galettes, cut into wedges, at room temperature.
Recipe courtesy of Gourmet Magazine