Coat fifteen 1-3/4-inch muffin cups with nonstick cooking spray or use a nonstick pan; set aside. Unroll phyllo dough. Remove one sheet of the phyllo dough and place it on cutting board. Cover remaining phyllo dough with plastic wrap.
Lightly brush phyllo sheet with melted butter; sprinkle with bread crumbs. Working quickly, top with the remaining phyllo sheets, coating each sheet with butter and bread crumbs.
Cut phyllo stack lengthwise into three 3-inch-wide strips. Cut each strip crosswise into five rectangles. Press each rectangle into a prepared cup, pleating as needed to fit. Bake in a 350 degree F oven for 6 to 8 minutes or until lightly golden brown. Cool in muffin cups for 5 minutes. Carefully remove phyllo cups from muffin cups; cool on a wire rack.
Just before serving, fill muffin cups with a generous teaspoon of sour cream or crème fraiche; top with about 1/2 teaspoon of caviar. Makes 15 tarts.
To shortcut this recipe, substitute one 2.1-ounce package baked miniature phyllo dough shells (15) for the phyllo dough. Prepare as directed, starting with step 3.
Prepare as directed through step 3. Place phyllo cups in a single layer in an airtight container; store at room temperature for up to 2 days.