Combine shredded cheddar and melted butter in a blender or food processor to make a "cheese paste".
In a medium bowl, combine flour, salt, sourdough starter, and cheese paste. Incorporate ingredients with your hands until thoroughly combined. Form a dough ball.
Let dough rest for 25 minutes to absorb liquid. (You can also leave in the fridge for up to 2 days wrapped in plastic. This makes a for a long fermented cracker.)
Roll out dough between two pieces of parchment paper. Dough should be about 1/16th of an inch thick.
Using a pizza cutter, cut dough into strips, then across to cut make squares. (Poke at least one hole in each cracker to prevent "puffing up" as they bake!)
Lightly sprinkle crackers with sea salt
Bake at 375ยบ for 16 minutes or until brown on the edges. Remove from oven and allow to cool. (They'll crisp up even more as they cool).
