Originally posted/ source: Bon Appetit
Preheat oven to 350°. Toast almonds on a rimmed baking sheet, tossing once, until golden brown and fragrant, 6–8 minutes. Let cool; pulse in a food processor until mostly finely ground but there are still bits of almond.
Mix almonds, flour, sugar, cornmeal, and salt in a large bowl, then add butter and vanilla and almond extracts and work in with your fingers or the handle of a sturdy wooden spoon. Scatter crumble, trying not to break it up too much, on a rimmed baking sheet and bake, tossing halfway through, until golden brown, 20–25 minutes. Let cool.
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.
Using an electric mixer, beat cream in a medium bowl until medium peaks form. Fold in almond extract, if using.
Divide warm apricots among plates. Spoon some whipped cream on top. Drizzle with honey and scatter fregolotta crumble over.