Bring a large pot of salted water to a rolling boil. Add the linguine and cook according to package directions until al dente. Before draining, reserve about 1/2 cup of the starchy pasta water. Drain the pasta and set aside.

While the pasta cooks, heat olive oil and butter in a large skillet or Dutch oven over medium heat. Add the minced shallot and cook until softened, about 2-3 minutes. Add the minced garlic and red pepper flakes (if using), and cook for another minute until fragrant, being careful not to burn the garlic.

Add the chopped kale to the skillet. It will seem like a lot, but it will cook down significantly. Cook, stirring frequently, until the kale has wilted and is tender, about 5-7 minutes.

Pour in the vegetable broth and bring to a simmer, scraping any browned bits from the bottom of the pan. Stir in the heavy cream and grated Parmesan cheese. Reduce heat to low and let the sauce gently simmer for 2-3 minutes to thicken slightly.

Add the cooked pasta to the skillet with the sauce and kale. Toss to coat evenly. Stir in the fresh lemon juice, salt, and black pepper. If the sauce seems too thick, add a splash or two of the reserved pasta water until it reaches your desired consistency.

Taste and adjust seasoning as needed. Serve immediately, garnished with extra grated Parmesan cheese and a squeeze of fresh lemon, if desired.