How to Make It
In a food processor, pulse the olives with the garlic and lemon zest until the olives are finely chopped. Add 1/4 cup of the olive oil and season with salt and pepper. Spread the olivada on the cut sides of the rolls.
In a small bowl, whisk the vinegar with the oregano and 1/2 cup of the olive oil. Season the dressing with salt and pepper.
Preheat a grill pan. In a large bowl, toss the zucchini with the remaining 1/4 cup of olive oil and season with salt and pepper. Grill the zucchini slices over high heat for about 5 minutes, turning once, until tender and lightly charred.
Mound the zucchini onto the rolls and drizzle with a little of the dressing. Top with the mozzarella, tomatoes and basil and drizzle with more of the dressing. Close the subs and serve right away.