In a large mixing bowl, whisk together the flour, salt, smoked paprika, and thyme to evenly distribute the spices.
Grate the fresh cheddar cheese directly into the dry mixture, using a coarse grater to ensure good melt and flavor.
Add the cold, cubed butter to the bowl. Using your fingertips or a pastry cutter, work the butter into the flour mixture until it resembles coarse crumbs with pea-sized bits.
Pour in 2 tablespoons of cold water, then gently mix with a fork or spatula. Add more water a teaspoon at a time until the dough just comes together when pressed.
Turn the dough onto a lightly floured surface and press it into a flat disk. Wrap snugly in plastic wrap and refrigerate for at least 30 minutes to relax the gluten and firm up the butter.
Preheat your oven to 180°C (350°F). Line a baking sheet with parchment paper. Remove the dough from the fridge and roll it out to about 1/8 inch thick with a floured rolling pin.
Use a sharp knife or cookie cutter to cut the dough into your desired shapes — rectangles, squares, or circles — and transfer them to the prepared baking sheet, spacing them evenly.
Brush the tops of the crackers lightly with the beaten egg to give them a shiny, golden finish. If desired, sprinkle a tiny pinch of extra salt or herbs on top.
Bake in the preheated oven for 12-15 minutes, or until the edges are golden brown and the crackers are crispy. Keep an eye on them to prevent over-browning.
Once baked, remove the crackers from the oven and transfer to a wire rack. Let them cool for at least 10 minutes—they will firm up as they cool and become irresistibly crunchy.
Enjoy your gourmet cheese crackers plain, or serve with dips. Store leftovers in an airtight container for up to a week to keep them crisp and flavorful.