Preheat oven to 350 degrees.
Place 1 sheet of phyllo dough on parchment paper (keep remainder covered w/ a damp paper towel). Use a pastry bruch, lightly coat the phyllo dough with some butter.
Place 2nd sheet on top and brush with more butter, repeat with the remaining phyllo and butter.
Coat four 4" tart pans (w/ removable bottoms) with nonstick spray.
Use a 6" pastry ring, cut out 4 circles from the phyllo dough. Fit each in a tart pan.
Place a circle of parchment paper in each pan, hold it down with rice or dry beans. Blind bake the pans on a baking sheet for 10 minutes, then remove from oven and remove weights carefully.
Raise the temperature to 375.
Spread 1 tbsp of jam on bottom of each tart, arrange 20 of the apricot slices in each, fitting them tightly. Sprinkle 1 tsp of sugar over the top of each tart.
Bake for 20 minutes, or until the apricots are cooked and the top if nicely glazed. Serve warm or at room temperature.