Start by sifting together the flour, salt, and black pepper in a small bowl. This step keeps everything evenly distributed so you don't end up with a salty bite in one spot and a bland one in another. Set this bowl aside while you prep the wet ingredients.
In a stand mixer, beat the softened butter and shredded cheddar together until fully combined. It will look a little like a chunky paste at first, but keep mixing until it turns smooth and creamy. This forms the flavorful base for your entire batch of crackers.
With the mixer running on low, slowly add in the flour mixture and continue beating until the dough forms a solid ball. Turn the dough out onto a lightly floured surface and knead it a few times by hand until it feels smooth and uniform throughout.
Wrap the dough tightly in plastic wrap and refrigerate it for about an hour. I know it's tempting to skip this step, but chilled dough rolls out far more evenly and holds its shape much better once it hits the oven.
Preheat your oven to 375°F and line a baking sheet with parchment paper. On a floured surface, roll the chilled dough out to about ⅛-inch thickness, then use a small cookie cutter to cut out rounds. Arrange them close together on the sheet since they won't spread much while baking.
Prick each cracker gently with a fork, then sprinkle the tops with flaky sea salt. Bake for 12 to 15 minutes, or until the edges turn a deep golden brown. Let them cool completely on the sheet before serving or storing.