Make the creamy sun-dried tomato pesto by placing the cashews, milk, ½ cup of the sun-dried tomatoes, lemon juice, garlic and salt into the bowl of a food processor fitted with an S-blade. Blend until smooth. Add the basil, walnuts, and remaining sun-dried tomatoes. Pulse until they're finely chopped and mixed into the cashew mixture. Taste test and season with additional salt if desired.

Bring a large pot of water to a boil. Add the pasta to the pot and cook for 6 minutes. Add the broccoli florets and cook 1 to 2 minutes more, until the pasta is tender and the broccoli is bright green and tender-crisp. Drain the pasta and broccoli into a colander.

Return the pasta and broccoli to the pot and add the creamy sun-dried tomato pesto. Toss to coat, adding more milk if needed.

Divide the pasta onto plates and top with additional basil and red-pepper flakes, if desired. Serve.