Line a rimmed baking sheet with parchment and preheat oven to 400 degrees F.
Arrange the tomatoes on prepared baking sheet. Drizzle with a little olive oil, sprinkle with salt and pepper, and toss to coat. Bake in preheated oven until the tomatoes start to darken, burst, and wrinkle, 45-60 minutes.
Allow the tomatoes to cool slightly, then transfer with any juices to a food processor. Add the almonds, tahini, vinegar, cumin, and cayenne. Process until combined, then keep running while slowly drizzling in the olive oil until the dip becomes smooth and creamy. Add a little more olive oil if needed. Season with salt and pepper to taste.
Serve with tortilla or pita chips.