1In a mini food processor, combine the basil, garlic and paprika and process until finely chopped. With the machine on, gradually pour in the 3 tablespoons of olive oil until blended. Season the pesto with salt.
2Light a grill. Brush the zucchini slices with olive oil and season with salt. Grill over high heat until nicely charred and just tender, about 2 minutes per side. Cut each zucchini slice in half crosswise.
3Grill the English muffins cut side down over low heat until just soft, about 30 seconds. Turn and grill until the muffins start to brown, about 1 minute. Spread the cut sides of the muffins with the pesto. Layer 1 slice of cheese, 2 zucchini pieces and 1 more slice of cheese on the bottom halves of each muffin. Close the sandwiches; brush the tops and bottoms with oil. Grill over low heat, turning, until they’re crisp on the outside and the cheese is melted, about 4 minutes total. Cut the sandwiches in half and serve.