In a food processor, add the carrot, celery and onion. Pulse several times until everything is finely chopped. Heat a large dutch oven or high-sided skillet over medium-high heat. Add the olive oil and the vegetables. Cook, stirring often, for about 5-6 minutes or until mixture is slightly drier and starting to brown lightly. Stir in the garlic, anchovies (if using) and tomato paste. Cook for another minute.
Add the sausage meat. Cook, breaking up meat, until just starting to brown (5-6 minutes). Add the crushed tomatoes. Fill can about 2/3 full of water, swish to collect all the tomatoes left in the can and add to pan. Season with salt and black pepper. Stir to combine. Bring to a boil. Reduce heat to a gentle simmer and cook for 25-30 minutes until sauce has thickened a bit.
While sauce is cooking, put a large pot of water on the stove to heat for pasta. In a food processor, add the ricotta cheese, salt and pepper. While machine is running, slowly stream in 3 tablespoons of olive oil. Taste and adjust seasoning as desired. Set aside.
Cook pasta according to package instructions for al dente pasta. Cook pasta 1-2 minutes less than time instructed. Drain, reserving 1-2 cups of the pasta cooking water. With pasta sauce simmering, add the drained pasta. Stir and cook gently for about 1 minute. Add a little pasta cooking water to loosen, if needed.
To plate: spread about 1/4 cup of the whipped ricotta to a bowl or plate. Spoon pasta over the ricotta. Garnish with parmesan, parsley and red chili flakes, if desired. Serve immediately.