In a food processor or large bowl, pulse or whisk together the flour, salt, paprika, and a few grinds of black pepper.
Add the cold, cubed butter. Pulse or use a pastry cutter to cut the butter into the flour until the mixture resembles coarse crumbs with some pea-sized pieces remaining.
Add the grated Parmesan and Cheddar cheeses and toss briefly to combine.
Drizzle the cold heavy cream over the mixture.
Mix gently with a fork or your hands just until the dough comes together into a smooth ball.
Do not overwork it.
Shape the dough into a flat disk, wrap it tightly in plastic wrap, and chill in the refrigerator for at least 1 hour.
Preheat your oven to 325°F / 165°C.
In a small bowl, beat the egg with 1 tablespoon (15 ml / 0.5 fl oz) of cold water to create an egg wash.
On a lightly floured surface, roll the chilled dough out to a rectangle approximately ⅛ to ¼ inch thick.
Cut the dough into strips about ½ inch wide and 1½ inches long.
Arrange the strips on ungreased baking sheets, leaving a little space between them.
Lightly brush the tops of the strips with the prepared egg wash.
Bake for 12 to 14 minutes, or until the pastries are puffed, golden, and just beginning to brown.
Let them cool for a minute on the sheet before transferring to a wire rack to cool completely.
Serve warm for the best experience.
Mix the dough just until it comes together. Overworking it can develop the gluten and make your cheese straws tough instead of tender.
