Process first 3 ingredients in a food processor just until blended. Add pieces of butter, pulsing 5 or 6 times or until mixture is crumbly.
Combine egg yolk, whipping cream, and vanilla; stir well. With processor running, slowly add egg mixture through food chute; process just until ingredients form a ball and leave sides of bowl. Shape dough into a flat disc; cover and chill 30 minutes.
Place 3/4 cup sugar in a large, heavy skillet. Cook over medium heat, stirring constantly with a wooden spoon, until sugar melts and syrup is golden. Remove from heat, and slowly add 3/4 cup cream, stirring gently. (Sugar may crack and harden, but will melt again.) Return to heat, and cook, stirring gently, until mixture is smooth and thickened. Remove from heat; stir in almond extract and sliced almonds. Cool.
Cut chilled dough in half; divide each half into 8 balls. Press each ball into a lightly greased 1 1/2" round tartlet pan; place tartlet pans on a baking sheet. Bake at 350° for 12 minutes. Cool slightly.
Increase oven temperature to 400°. Fill each tartlet shell with 1 tablespoon almond filling. Bake at 400° for 14 to 18 minutes or until golden. Cool completely on a wire rack. Remove from pans.
Note: For variety, we baked some of the tartlets in 4" x 2" barquette (boat-shaped) molds. We reduced the baking times for the crust and tartlets each to 9 minutes.