Preheat oven to 375°F.
Make béchamel sauce: Melt butter in a saucepot over medium heat. Whisk in flour, bring roux to a bubble then whisk in milk. Let thicken 2-3 minutes; season with salt. Melt in pieces of Taleggio until fully incorporated then stir in Parmigiano-Reggiano. Add the ricotta a little at a time. Once fully incorporated, stir in chili flakes and remove from heat; let cool.