Heat the oven to 375°F (190°C) and lightly grease a 9×13-inch baking dish. Put the Brie in the freezer for about 10 minutes while preparing the dough, just to firm it up for cutting.
Unroll both tubes of crescent dough into two rectangles. Press the perforated seams closed. Cut each rectangle into 12 roughly equal pieces, making 24 pieces total.
Cut the chilled Brie into 24 small pieces, roughly ½ to ¾ inch across. Leave the rind on, or trim it away first if preferred. Divide the cheese evenly across the dough pieces.
Place one piece of Brie in the center of each dough square. Top each with about 1 teaspoon of preserves, using ½ cup across the batch. Keep the filling away from the edges.
Bring the four dough corners up around the filling and gently pinch them together near the top. A little cheese or jam showing is fine. Press any open seams closed without stretching the dough until it tears.
Place the filled bites snugly in the prepared dish in a single layer. Four across and six down is a useful arrangement for 24 bites.
Bake for 15 to 20 minutes, beginning to check at 15 minutes. The dough should be puffed, golden brown, and baked through, including the folds near the center of the dish. Adjust the time to doneness.
Let the bites rest in the dish for 5 to 10 minutes so the hot filling can settle. Lift them out with a small spatula and serve warm while the Brie is still soft.