Use six 3- to 4-inch tartlet rings or fluted tartlet pans. Roll the dough into a 10-inch rectangle and line the tartlet rings or pans with it. Refrigerate the tartlet shells. Preheat the oven to 300°F.
If you're using fresh apricot halves, sprinkle them with 2 tablespoons of the granulated sugar and saute them in 2 tablespoons of the butter over medium heat for about 10 minutes, or until soft and lightly browned. Let cool.
Spread about 2 tablespoons of the frangipane in each of the lined tartlet rings and arrange the apricot halves, overlapping, on top (see Note). Brush the apricots with the melted butter and sprinkle with 1 tablespoon of the granulated sugar. Bake for about 45 minutes, or until the tartlets are golden brown on the edges.
Brush with glaze as soon as they come out of the oven, or just before serving, dust with confectioners' sugar.

Note: If the apricots are ripe and sweet, use less sugar when sautéing. You can also cut the apricot halves into wedges and arrange them.