Pulse the cauliflower with the butter and cream in a food processor to a coarse consistency. Add the cheese and season with salt and pepper. Whip the egg white to a stiff peak in a bowl, and then fold into the cauliflower mixture to lighten it up. For best results, chill for about 30 minutes so they hold their shape.
Preheat the oven to 375 degrees F.
Roll a spoonful of the mixture in the breadcrumbs, shape into tater tots using your hands and put on a baking sheet lined with parchment paper.
Bake until slightly browned, about 15 minutes. Serve.