Prepare a grill for medium heat. Brush the cut side of each apricot half with oil and grill apricots, cut side down, until lightly charred and juices start to seep out of fruit, 6–8 minutes.

Using a metal spatula, carefully turn apricots, and grill a minute or so until the other side is lightly charred. Transfer to a plate. Lightly sprinkle with coconut sugar.

Using an electric mixer, beat cream until almost thick, then add in the mascarpone cheese, almond extract, and powdered sugar. Beat for 30 seconds until medium peaks form.

Divide warm apricots among plates. Spoon whipped cream on top. Optional for garnishing: Drizzle with honey and a few toasted walnuts or pecans.