Preheat oven to 400°F (200°C).

In the work bowl of a food processor, pulse flour and pine nuts until nuts are coarsely chopped. Add cheese, chives, basil, and kosher salt, and pulse until combined. Add ⅓ cup (80 grams) water and oil, and pulse until combined and a dough forms. Turn out dough onto a lightly floured piece of parchment paper, and divide in half. Transfer half of dough to another piece of floured parchment paper.

Roll half of dough into a square that is at least 9 inches but no larger than 12 inches. (The larger your square, the thinner and crisper your crackers will be; see Note.) Using a sharp knife or pastry wheel, cut dough into 1½- inch diamonds. Slide parchment with crackers onto a rimmed baking sheet. Sprinkle with sea salt. Repeat with remaining dough.

Bake, one pan at a time, until golden brown, 8 to 10 minutes. (If the center crackers on the sheet are lighter than the edges, break apart the crackers, rearrange them, and bake for 2 to 3 minutes more.) Let cool on pan for 10 minutes. Gently break apart crackers, and let cool completely on a wire rack. Store in an airtight container for up to 5 days.