Roughly chop the cucumber, pepper, onion, and garlic. Place all of these vegetables in the bowl of a food processor. (I put the chopped garlic on top so it is less likely to get stuck under the blade.) Pulse to finely chop the vegetables, scraping down the sides once or twice. Do not puree. You want a little texture. Transfer the mixture to a large bowl.
Roughly chop the tomatoes, and place in the food processor. (No need to rinse the work bowl.) Puree until smooth. (You can keep a little chunkiness to the tomatoes if you like, but I like to keep this part on the smoother side.) Add to the cucumber mixture.
Stir in the olive oil, vinegar, salt, pepper, cumin, sugar, and cayenne pepper. Cover and refrigerate for several hours or, ideally, overnight.
Serve with desired toppings.