Shred cheese and butter with the grater attachment of a food processor. Exchange the grater for the blade and add salt. Process for 20 seconds. Add flour and process 10 seconds. Stream in ice water slowly until dough forms a ball.
Divide the dough in two and form two flat discs. Wrap tightly in plastic wrap and chill for 30 minutes.
Preheat oven to 350°. Roll out one disc on a piece of parchment paper using plastic wrap on top to prevent sticking until it is about a 12 x 8 rectangle and a 1/8 inch thickness. Use a pastry wheel to cut out one inch squares. Place a center dot in each with the back end of a skewer. Sprinkle coarse sea salt with a light hand. Place parchment with cut crackers onto a baking sheet. There is no need to separate crackers so save yourself some trouble. Repeat with the other disc. If the oven isn’t ready, place the prepared crackers in the refrigerator to keep cold until you’re ready to bake.
Bake for about 18 minutes, until crackers smell wonderful and they just barely start to brown. You may want to check on them starting at about 16 minutes, because they have the potential to burn quickly at the end. Carefully transfer the parchment to a cooling rack.
Allow crackers cool, then gently break them apart. Enjoy immediately or store them in an air-tight container for up to a week.