Special equipment: 6 mini Bundt pans; a squeeze bottle
For the angel food cake: Preheat the oven to 350 degrees F. Grease and flour 6 mini Bundt pans.
Sift the confectioners' sugar, cake flour and salt onto a sheet of parchment paper. Sift again.
Beat the egg whites in a large bowl with an electric mixer on medium speed until frothy. Add the cream of tartar and beat until soft peaks form, about 5 minutes. Gradually beat in the granulated sugar, about 1 tablespoon at a time. Increase the speed to medium-high and continue beating until stiff, shiny peaks form, 12 to 15 minutes. Add the vanilla and beat a few seconds to combine.
Sprinkle one-quarter of the flour mixture over the egg white mixture and gently fold with a rubber spatula. Fold in the remaining flour mixture in 3 additions. Transfer the batter to the prepared Bundt pans.
Bake until the cakes feel springy and a toothpick inserted into the center comes out clean, 40 to 50 minutes. Invert the pans onto a funnel or the neck of a bottle and let cool completely. Loosen the edges of the cakes with a small knife, tap the sides of the pans against the counter, and unmold.
For the strawberry sauce: Add the strawberries, sugar and lemon juice to a small saucepan over medium heat. Cook, stirring, until the strawberries have broken down and the mixture is soupy, about 15 minutes. Transfer to a blender and pulse until smooth. Strain back into the pot. Bring to a boil and stir in the cornstarch, making sure to avoid lumps. Remove from the heat and stir in the butter. Allow to cool, then transfer to a squeeze bottle.
For the brown sugar-creme fraiche whipped cream: Whip the cream until firm peaks form using a whisk or electric mixer. Fold in the creme fraiche and brown sugar.
For the crumbs: Preheat the oven to 300 degrees F. Line a rimmed baking sheet with parchment.
Combine the flour, granulated sugar, light brown sugar, baking powder and salt in a medium bowl. Add the oil and vanilla. Using your hands, mix until no dry spots remain and large clumps form when mixture is pressed together. Break up the mixture into clusters (some small, some large) and spread onto the prepared baking sheet.
Bake, stirring occasionally, until the crumble is light golden brown and crunchy, 10 to 12 minutes. (It will get crunchier as it cools.) Let cool completely.
Place the cakes on serving plates. Top with strawberry sauce, whipped cream and crumbs.