PreparationFor pear compote: Combine 3/4 cup sugar, 1/2 cup water, lemon juice, 3/4 teaspoon lemon peel, and 3/4 teaspoon thyme in medium saucepan. Stir over medium heat until sugar dissolves and mixture boils. Remove saucepan from heat; cover. Let steep 10 minutes. Pour syrup through fine strainer set over bowl. Return syrup to saucepan. Add 3/4 teaspoon lemon peel and 3/4 teaspoon thyme and bring to simmer. Add pear cubes and simmer over medium heat until pears are tender but still hold shape, about 10 minutes. Using slotted spoon, transfer pear to rimmed baking sheet. Boil syrup in saucepan until reduced to 1/3 cup, about 5 minutes. Transfer reduced syrup to blender. Add 1/3 cup pear pieces; puree until smooth. Transfer pear puree to medium bowl. Add remaining pear pieces to puree. DO AHEAD: Can be made 1 day ahead. Cover and chill. For cake: Preheat oven to 325°F. Butter 8-inch-diameter cake pan with 2-inch-high sides. Line bottom of pan with parchment paper; butter parchment. Whisk 1 cup plus 2 tablespoons flour, 11/2 teaspoons baking powder, and 1/2 teaspoon salt in medium bowl to blend. Using electric mixer, beat 3/4 cup sugar and 1/4 cup butter in large bowl until well blended. Add egg and egg yolk and beat until blended. Add flour mixture in 2 additions alternately with buttermilk in 1 addition. Beat in 1/2 teaspoon vanilla, then fold in 2 tablespoons crème fra&ircirc;che. Transfer batter to prepared cake pan; smooth top. Bake cake until golden around edges and tester inserted into center comes out with some moist crumbs attached, about 45 minutes. Remove from oven and cool cake in pan on rack 15 minutes. Maintain oven temperature. Invert cake onto tart pan bottom or flat platter. Peel off parchment paper. Butter same cake pan and line bottom with clean parchment paper. Spread pear compote evenly over parchment paper in pan. Carefully return cake to pan, placing bottom side down atop compote. Return to oven and bake until cake is golden and tester inserted into center comes out clean, about 15 minutes. Cool cake in pan 5 minutes. Invert cake onto platter; remove pan. Cool cake at least 20 minutes. Cut cake into wedges. Serve warm with Greek Yogurt Ice Cream alongside.
PreparationFor pear compote: Combine 3/4 cup sugar, 1/2 cup water, lemon juice, 3/4 teaspoon lemon peel, and 3/4 teaspoon thyme in medium saucepan. Stir over medium heat until sugar dissolves and mixture boils. Remove saucepan from heat; cover. Let steep 10 minutes. Pour syrup through fine strainer set over bowl. Return syrup to saucepan. Add 3/4 teaspoon lemon peel and 3/4 teaspoon thyme and bring to simmer. Add pear cubes and simmer over medium heat until pears are tender but still hold shape, about 10 minutes. Using slotted spoon, transfer pear to rimmed baking sheet. Boil syrup in saucepan until reduced to 1/3 cup, about 5 minutes. Transfer reduced syrup to blender. Add 1/3 cup pear pieces; puree until smooth. Transfer pear puree to medium bowl. Add remaining pear pieces to puree. DO AHEAD: Can be made 1 day ahead. Cover and chill. For cake: Preheat oven to 325°F. Butter 8-inch-diameter cake pan with 2-inch-high sides. Line bottom of pan with parchment paper; butter parchment. Whisk 1 cup plus 2 tablespoons flour, 11/2 teaspoons baking powder, and 1/2 teaspoon salt in medium bowl to blend. Using electric mixer, beat 3/4 cup sugar and 1/4 cup butter in large bowl until well blended. Add egg and egg yolk and beat until blended. Add flour mixture in 2 additions alternately with buttermilk in 1 addition. Beat in 1/2 teaspoon vanilla, then fold in 2 tablespoons crème fra&ircirc;che. Transfer batter to prepared cake pan; smooth top. Bake cake until golden around edges and tester inserted into center comes out with some moist crumbs attached, about 45 minutes. Remove from oven and cool cake in pan on rack 15 minutes. Maintain oven temperature. Invert cake onto tart pan bottom or flat platter. Peel off parchment paper. Butter same cake pan and line bottom with clean parchment paper. Spread pear compote evenly over parchment paper in pan. Carefully return cake to pan, placing bottom side down atop compote. Return to oven and bake until cake is golden and tester inserted into center comes out clean, about 15 minutes. Cool cake in pan 5 minutes. Invert cake onto platter; remove pan. Cool cake at least 20 minutes. Cut cake into wedges. Serve warm with Greek Yogurt Ice Cream alongside.