Heat oven to 350° F. Butter a 9-inch removable-bottom fluted tart pan.
In a food processor, process the almonds and ½ cup of the sugar until finely ground. Add the butter, egg, and almond extract and process until smooth. Add the flour, baking powder, and salt and pulse a few times just to combine (the dough will be soft).
Spread the dough in the bottom of the prepared pan.
In a small bowl, toss the pears and apricots with the lemon juice and the remaining tablespoon of sugar. Arrange the pears in the dough. Scatter the apricots over the dough, pressing them in gently.
Bake until the pears are tender and the center is firm, 50 to 55 minutes (cover the edges with foil if they brown too quickly).
In a small bowl, combine the preserves and 1 tablespoon water. Brush over the warm tart. Let cool in the pan before unmolding.