Grilled Gruyère-and-Zucchini Sandwiches with Smoky Pesto

packed cup basil leaves

large garlic clove, coarsely chopped

hot smoked paprika

extra-virgin olive oil, plus more for brushing

Salt

zucchini, cut into 4 lengthwise slices

English muffins, preferably Bays, split

Gruyère or Appenzeller cheese, cut into 8 thin slices