In a mixing bowl, combine the butter and sharp cheddar cheese. Use a standing mixer or an electric mixer to mix on medium/high speed for 4-5 minutes until the mixture is smooth, combined, and fluffy.
Add 1 teaspoon of salt to the flour and whisk together. Gradually add the flour mixture to the cheese mixture on low speed until it turns into a dry crumble.
Gradually add cold water by the teaspoon until a dough forms.
Form the dough into a ball, flatten it into a disk, and wrap it in plastic wrap. Refrigerate for at least 1 hour.
Preheat the oven to 375°F (190°C). Roll the dough out on a piece of parchment paper into a rectangle less than ⅛ inch thick. Use a ruler to mark 1-inch squares and cut with a pizza cutter or pastry cutter.
Use a wooden skewer to poke a hole in the center of each square. Transfer the parchment paper with the dough squares to a baking sheet, ensuring they do not touch.
Brush each square with olive oil and sprinkle with additional kosher salt.
Bake for 15-17 minutes or until golden brown. Remove from the oven and transfer the parchment paper to a cooling rack immediately.