How to Make It
Lightly oil an 8-by-8-inch baking dish. Line the dish with a sheet of wax paper that extends 4 inches beyond the rim.
Strain the apricot syrup from the can into a saucepan; reserve the apricots. Add the dried apricots to the saucepan and bring to a boil. Reduce the heat and simmer until the apricots are tender and most of the liquid has evaporated, 7 minutes.
Transfer the contents of the saucepan to a food processor. Add the reserved canned apricots, the apricot preserves and the 1/2 cup of sugar. Process until smooth. Transfer the apricot puree to the saucepan and boil over moderately high heat, stirring often, until it has thickened and any excess liquid has evaporated, about 8 minutes.
In a bowl, sprinkle the gelatin over the water in an even layer. Let stand until the gelatin softens, then microwave the water for 20 seconds to dissolve the gelatin completely. Stir the gelatin into the apricot puree. Scrape the mixture into the prepared dish and smooth the surface. Let cool to room temperature, then cover with plastic wrap and refrigerate overnight.
Just before serving, unmold the apricot pâte de fruit onto a work surface. Peel off and discard the wax paper. Using a sharp knife, cut the pâte into 1-inch squares or triangles. Spread about 1/2 cup of sugar in a shallow bowl. Roll the pieces in the sugar to coat. Arrange on a platter and serve.