Make crust: Mix 1 cup flour, 1 tablespoon sugar and 1/4 teaspoon salt in processor. Add butter; cut in using on/off turns until coarse crumbs form. Add 3 tablespoons water. Process until small moist clumps form, adding more water by teaspoonfuls if dry. Gather dough into ball; flatten into disk. Wrap dough in plastic. Chill until cold, about 1 hour.
Roll out dough between 2 sheets of plastic wrap to 11-inch round. Remove top sheet of plastic. Using bottom sheet of plastic as aid, invert dough into 9-inch-diameter tart pan with removable bottom. Using plastic wrap, press dough into tart pan. Remove plastic. Fold overhanging dough in; press to form high-standing, double-thick sides. Pierce dough all over with fork. Freeze 30 minutes. (Can be prepared 1 day ahead. Cover dough and keep frozen.)
Preheat oven to 400°F. Bake crust until golden, about 25 minutes. Cool on rack. Maintain oven temperature.
Make filling: Combine 1/4 cup butter and almond paste in processor and blend until smooth. Add egg and process until well blended. Add flour and process just until blended. Spread filling evenly over bottom of crust. Toss apples with sugar in large bowl. Arrange apples in concentric circles atop filling. Brush apples with melted butter.
Place tart on baking sheet. Bake until apples are tender and light golden, about 40 minutes. Transfer to rack; cool 15 minutes. Brush apples with honey. Serve warm or at room temperature.