Bring a large pot of water to a rolling boil over high heat. Once boiling, add salt and gently toss in the tagliatelle pasta. Cook according to package instructions until al dente, about 8-10 minutes. Reserve ½ cup of the pasta water before draining the pasta and set aside.

Heat a large skillet over medium heat. Add 2 tablespoons of extra virgin olive oil and 1 tablespoon of unsalted butter, allowing them to melt and blend. Add the minced garlic, anchovy fillets, and red pepper flakes; cook for 2-3 minutes until fragrant.

Gently fold in the lump crab meat, warming through for about 1 minute. Pour in ⅓ cup of dry white wine, scraping the skillet to deglaze. Season with kosher salt and cook for an additional minute.

Add the drained tagliatelle pasta into the skillet. Squeeze in lemon juice and zest, then add parsley, dill, capers, and grated Parmesan. Toss gently to coat the pasta with the sauce.

Pour in the reserved pasta water and slowly stir in ¼ to ½ cup of heavy cream, adjusting for sauce consistency. Continue cooking for 1-2 minutes to thicken, then garnish with black pepper, additional Parmesan, and parsley before serving.