2 cups coarsely chopped pitted green olives (castelvetrano olives), divided=1 cup and 1 cup.
3 tablespoons capers, drained
1 tablespoon red wine vinegar
1 teaspoon anchovy paste
1 tablespoon Dijon mustard
1/4 teaspoon dried crushed red pepper
1/2 cup plus 1 tablespoon extra-virgin olive oil
1 pound gemelli, fusilli, or rotelle pasta
2 pints cherry tomatoes or grape tomatoes, halved
1 8-ounce fresh mozzarella diced into small cubes
2 tablespoons chopped fresh oregano
With machine running, add garlic clove to processor through feed tube and process until finely chopped; turn off machine. Add 1 cup chopped olives, capers, red wine vinegar, anchovy paste, mustard, and crushed red pepper. Using 6 on/off turns, process to chop coarsely. With machine running, gradually add 1/2 cup olive oil, forming coarse puree. Transfer to bowl; stir in remaining 1 cup olives. Season olivada to taste with salt and pepper. DO AHEAD Olivada can be made 3 days ahead. Cover and refrigerate.
Cook pasta in large pot of boiling salted water until just tender but still firm to bite, stirring occasionally. Drain well. Transfer drained pasta to large bowl. Drizzle remaining 1 tablespoon oil over pasta; toss to coat. Cool, stirring occasionally.
Add olivada, halved tomatoes, mozzarella, and oregano to pasta; toss to coat. Season to taste with salt and pepper.