Pulse the sun-dried tomatoes, Parmesan, pine nuts, garlic, basil, tomato paste, lemon juice, and red pepper flakes in a food processor until the mixture is roughly chopped and begins to come together.
Drizzle the olive oil into the mixture while blending until smooth and spreadable. You may have to stop to scrape down the sides as needed. Feel free to add additional oil until you reach your desired consistency.
Taste and season with salt and black pepper.
Serve immediately or store in an airtight container in the refrigerator.
Notes
Adjust texture with a little more olive oil if you prefer a looser pesto.