In the bowl of a food processor, place the 4 ounces Cheddar cheese, 2 ounces Parmesan cheese, 3/4 cup flour, 1/4 teaspoon dry mustard, 1/4 teaspoon kosher salt, and 1/8 teaspoon cayenne pepper. Pulse 5 times.
Add the 4 tablespoons (2 oz) unsalted butter and pulse again until the butter pieces are the size of BB's. Add the water, 1 tablespoon at a time, and pulse just until the dough holds together. If the dough is still crumbly, add more water, 1 teaspoon at a time, until it reaches the right consistency.
Turn the dough out onto a large piece of wax or parchment paper. Roll the dough into a log 9 or 10 inches long and square off the ends. Wrap well and refrigerate for at least 2 hours and up to 2 days. (You can freeze the dough for up to 1 month. You may want to cut the log in half or in thirds prior to freezing if you think you'll want to defrost a small amount at a time.)
Preheat the oven to 375°F (190°C). Line a baking sheet with parchment paper.
Cut the log into 1/4-inch-thick slices. Arrange the slices about 1 inch apart on a baking sheet. Bake for 8 to 10 minutes, or until the crackers are a light golden color. Turn the crackers and bake for 3 to 5 more minutes, until they are golden around the edges.
Cool the crackers on a wire rack. Serve at room temperature.