Begin by bringing a tall pot of water boiling.
While water is boiling, heat the oven to "broil".
Lay artichokes, garlic, and onions on a baking sheet. Drizzle the olive oil all over and roll the artichokes, garlic, and onions in the oil until nicely covered.
Sprinkle a few pinches of red pepper flakes over the artichoke and garlic (optional).
Roast while keeping a good eye on the artichokes so they don't burn black. When there is a nice brownish color on the artichokes, remove them from the oven and set them aside, covered to stay heated. Add a drizzle of olive oil and very gently stir so that the pasta doesn't stick together while you prepare the rest of the recipe.
Boil the pasta until al dente and even a little less than that.
In a large skillet, melt the butter, add the cream, lemon juice, and zest. Simmer at a warm temperature. Then add the parmigiana cheese. When the cheese is melted into the mixture, give it a good taste, and add more of any ingredient, if desired.
Add the roasted artichokes, garlic, and onions to the sauce, and heat through completely.
Place the pasta on a nice serving platter and then pour about half of the sauce on the pasta. Sprinkle freshly minced parsley and lemon zest all over the top. Serve.
Have a serving bowl with extra artichoke lemon parmigiana sauce and allow guests to add more sauce to their pasta.