In a food processor, combine flour, cheddar cheese, cold butter, salt, garlic powder, and onion powder. Pulse until the mixture forms coarse crumbs.
Add the sourdough starter discard and pulse until a soft dough forms.
Turn the dough out onto a lightly floured surface and knead briefly until smooth.
Divide the dough into two equal disks, wrap each in plastic wrap, and refrigerate for 30 minutes.
Preheat the oven to 350°F (175°C) and line two baking sheets with parchment paper.
Roll one disk of dough between parchment sheets to about 1/8-inch thickness.
Brush the surface lightly with olive oil, then sprinkle evenly with everything bagel seasoning and optional flaky sea salt.
Cut the dough into 1-inch squares using a pizza cutter or sharp knife, then transfer to the baking sheets leaving small spaces between.
Repeat the rolling, seasoning, and cutting steps with the second dough disk.
Bake the crackers for 16 to 18 minutes, rotating baking sheets halfway through until golden and crisp.
Cool crackers completely on a wire rack to develop extra crispiness.