Add the flour, salt, paprika, and cold butter cubes into your food processor. Pulse a few times until the mixture looks like coarse, sandy crumbs. Toss in the freshly grated cheddar and pulse again until it's evenly distributed through the flour mixture.
With the processor running, drizzle in the cold water one tablespoon at a time. Stop as soon as the dough clumps together into a rough ball. I never add all the water at once, since too much moisture makes the dough sticky and hard to roll.
Turn the dough out onto plastic wrap and pat it into a flat disc. Wrap it tightly and refrigerate for about 20 minutes. This resting time firms up the butter again, which is what gives these crackers their flaky bite.
Dust your countertop with flour and roll the chilled dough to about ⅛ inch thick. Press your star cutter into the dough, dipping it in flour between cuts if it starts sticking. Gather the scraps and re-roll until the dough is used up.
Arrange the stars on a parchment-lined baking sheet, leaving a little space between each one. Bake at 350°F for 15 to 18 minutes, until the edges turn golden and the centers feel firm to the touch.
Let the crackers rest on the tray for a minute or two, then transfer them to a wire rack. Cooling them fully is what makes them turn from soft to properly crunchy, so don't skip this part.