Preheat the oven to 350 degrees. Line a large sheet pan with parchment paper.
Mix together the flour and everything bagel seasoning in a medium mixing bowl. Pour in extra virgin olive oil, using a fork to combine. The mixture will be crumbly. Add in 1 tablespoon water at a time, mixing with your hands, until a ball forms and holds together.
Lightly dust your work surface with flour. Using a rolling pin, roll out dough on a baking mat or between two sheets of wax paper. Roll until dough is a thin sheet. Using small cookie cutters or a pizza cutter to cut into desired shapes.
Place cracker dough on the baking sheet, careful not to overlap pieces. Use a toothpick to poke 1-2 holes in each cracker.
Bake on the middle oven rack for 15 to 20 minutes, or until lightly browned. Smaller crackers will be done more quickly than regular sized crackers- be sure to check on them frequently to avoid burning!
Remove from oven and allow to cool on racks. Store at room temperature in an airtight container for up to 5 days.
Everything bagel seasoning: I use Trader Joe's everything but the bagel seasoning. If using a salt-free seasoning, I recommend adding a pinch or two of salt to the crackers.
For best quality, store leftover crackers in a closed container at room temp for 4-5 days.