Place ricotta, 1 tablespoon granulated sugar, and vanilla in a medium bowl; beat with a mixer at medium speed until well blended. Cover and chill.
Combine 2 tablespoons granulated sugar and hazelnuts. Stack 2 phyllo sheets on a large cutting board or work surface (cover remaining sheets to prevent drying); brush with half of butter. Sprinkle phyllo stack with half of hazelnut mixture. Repeat procedure with 2 phyllo sheets, remaining butter, and remaining hazelnut mixture. Top with remaining 2 phyllo sheets. Gently press phyllo layers together. Lightly coat top phyllo sheet with cooking spray. Cut stack into 6 (7 x 6-inch) rectangles. Carefully place 1 layered rectangle into each of 6 (8-ounce) ramekins coated with cooking spray. Gently press rectangles into ramekins to form baskets (phyllo will extend about 1 inch over tops of ramekins). Place ramekins on a baking sheet. Bake at 350º for 20 minutes or until lightly browned and crisp. Cool in ramekins on a wire rack. Carefully remove phyllo baskets from ramekins.
Just before serving, spread about 1 tablespoon cheese mixture into the bottom of each phyllo basket. Combine peaches and melted jelly, tossing to coat. Spoon about 1/2 cup peach mixture into each phyllo cup. Sprinkle evenly with powdered sugar. Serve immediately.