PASTA
Cook pasta according to package directions in salted water. Make sure to reserve some of the pasta water before draining, at least 1/2 cup. You will not use all of it but just in case.
TO MAKE THE PESTO
Add the sun dried tomatoes, walnuts, parmesan, basil, lemon juice, garlic, salt, and pepper to a food processor. Pulse until everything is broken up well but still chunky. Add the olive oil and pulse a few more times just until all mixed. Do not over-blend.
TO MAKE THE PASTA SAUCE
In a pan over medium heat, add the butter and olive oil. Melt down the butter until it starts to foam. After it foams, it will start to form brown bits. At the point, add the garlic and saute for about a minute.
Then add the sun dried tomato pesto along with the heavy cream. Mix all together.
It will appear to be a very thick sauce. Add the grated parmesan and pasta water and mix again. Taste and add salt and black pepper as needed. I did not need to add any salt since the pesto has salt along with the pasta water and parmesan.
Take off the heat and add the pasta, whole or chopped sun dried tomatoes, chopped basil, parsley, and more grated parmesan. Mix all together and serve warm!