1. Preheat oven to 400°.
2. To prepare crust, coat a 9-inch round removable-bottom tart pan with cooking spray; set aside. Weigh or lightly spoon 6.75 ounces flour into dry measuring cups; level with a knife. Combine 6.75 ounces flour, 2 tablespoons sugar, cinnamon, and salt in a food processor; pulse to combine. With processor on, gradually add butter through food chute, processing until mixture resembles wet sand. Combine vanilla and egg in a small bowl; stir with a whisk. With processor on, gradually add egg mixture, processing until dough forms. Turn dough out into prepared pan; gently press into bottom and up sides of pan. Chill 30 minutes.
3. To prepare filling, thinly slice figs to measure 1 1/2 cups; cut remaining figs into (1/2-inch) pieces (about 5 cups). Combine fig pieces, 1/4 cup sugar, and 2 tablespoons flour, tossing to coat figs. Spoon fig mixture into prepared crust. Bake at 400° for 20 minutes; reduce oven temperature to 350° (do not remove tart from oven). Bake an additional 25 minutes or until bubbly. Remove from oven; arrange fig slices over top of tart.
4. Place honey in a microwave-safe bowl. Microwave at HIGH 1 minute; brush over fig slices. Cool tart slightly on a wire rack. Serve warm with yogurt.