Preheat oven to 400°F.

In the bowl of a stand mixer fitted with the whisk attachment, beat cream, granulated sugar, and vanilla at high speed until soft peaks begin to form. Cover and refrigerate until serving.

Line a baking sheet with parchment paper. Sprinkle a small amount of flour onto a dry work surface. Roll puff pastry to ⅛-inch thickness. Using a 3-inch round cutter dipped in flour, cut puff pastry into 12 rounds. Place rounds on prepared pan. Place a second baking sheet on top of rounds, and place pans in oven.

Bake until lightly browned, about 30 minutes. Let cool completely.

Transfer chantilly cream to a piping bag fitted with a small tip. Pipe cream over surface of a pastry round. Top with another pastry round, and repeat process of adding cream, ending with one pastry round. Dust tops of mille feuilles with confectioners’ sugar. Top with blood orange sections and almonds just before serving.