Preparation

• For tomato confit:
  Preheat oven to 300°F. Oil large rimmed baking sheet. Arrange tomatoes on baking sheet. Scatter thyme sprigs and garlic cloves over. Drizzle with 1/2 cup olive oil, then sprinkle with coarse sea salt.
  Bake tomatoes 45 minutes. Turn tomatoes over; continue to bake until tomatoes shrink slightly but are still plump and moist, about 1 hour longer. Cool completely. Peel off skins. (Can be prepared 1 day ahead. Cover and refrigerate. Bring to room temperature before using.)
  For marinated tomatoes:
  Bring large pot of water to boil. Add tomatoes; blanch 30 seconds. Drain. Cool tomatoes. Peel, quarter, and seed tomatoes. Cut away membranes. Transfer tomatoes to glass jar or bowl. Add thyme, garlic cloves, and salt. Pour enough oil over tomatoes to cover. Let stand at room temperature 2 hours. (Can be made 1 day ahead. Chill. Bring to room temperature before using.)
  For crust:
  Blend flour and salt in processor. Using on/off turns, cut in butter until coarse meal forms. Add 2 egg yolks and 1 tablespoon water; process just until moist clumps form, adding more water if dry. Gather dough into ball; flatten into disk. Wrap in plastic and chill 2 hours. (Can be made 1 day ahead. Keep chilled. Soften slightly at room temperature before rolling out.)
  Preheat oven to 375°F. Roll out dough on lightly floured parchment paper to 12-inch round. Transfer parchment with crust to baking sheet. Pierce crust all over with fork; brush with egg glaze.
  Bake until crust is golden brown, about 27 minutes. Cool crust completely on parchment on baking sheet.
  For salad topping:
  Toss greens with oil and sea salt in large bowl. Place crust on platter. Arrange greens atop crust, leaving 1-inch plain border.
  Starting at outside edge and working toward center, alternate tomato confit and marinated tomatoes in slightly overlapping concentric circles atop greens. Top with Parmesan shavings.
  Garnish with basil leaves. Cut into wedges and serve.