Put an oven rack in the center of the oven. Preheat the oven to 400 degrees F.

Spray 2 baking sheets with cooking spray. Lay the pancetta in a single layer on the prepared baking sheets and bake until crispy and brown, about 12 to 14 minutes. Drain on paper towels. Cool for 5 minutes and crumble. Set aside.

In a food processor, combine the butter, cheeses, salt, and 1 tablespoon vegetable oil. Blend until smooth, adding extra oil, as needed, until the mixture is spreadable. Add the spinach and pulse until just combined.

Preheat a panini maker. Spread the cheese mixture over 8 slices of bread. Top with the crumbled pancetta. Put the remaining bread slices on top. Grill the sandwiches, 2 at a time, until golden and crispy, about 3 to 4 minutes. Cool for 2 minutes, then cut each sandwich in half and arrange on a platter.