1. Adjust oven rack to upper- and lower-middle positions and heat oven to 425 degrees. Line 2 rimmed baking sheets with parchment paper. Remove and discard tomato cores. Slice tomatoes in half through core and place, cut-side up, on prepared baking sheets. Drizzle 1/2 cup of oil evenly over tomatoes, and season with garlic, herbs de Provence, salt, and pepper. Flip tomatoes cut-side down, transfer to oven, and bake until skins have loosened, about 30 minutes.
2. Remove tomatoes from oven and reduce oven temperature to 300 degrees. Pour off any liquid in bottom of pan into medium bowl. Using tongs, carefully remove and discard tomato skins. Return tomatoes to oven for 30 minutes.
3. Remove tomatoes from oven and pour off any liquid into bowl. Using tongs, carefully flip each tomato half and return to oven until tomatoes are visibly shrunken, dry, and slightly dark around edges, 2 to 2 1/2 hours, pouring off liquid as necessary every 30 minutes.
4. Transfer baking sheets to wire rack, and allow tomatoes to cool to room temperature. Transfer tomatoes to clean bowl and cover completely with remaining olive oil. Cover bowl with plastic wrap and refrigerate for up to 4 weeks. (If freezing tomatoes, do not cover with oil; transfer to zipper-lock freezer bags and freeze for up to 3 months.) Reserve tomato liquid for another use.
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