Bring a large pot of salted water to a rolling boil and add the pasta, stirring occasionally until it reaches al dente (follow package directions). While the pasta cooks, heat the olive oil and butter in a large skillet over medium heat until the butter is foaming. Add the prosciutto strips and cook for 3-4 minutes, stirring occasionally, until the edges are crispy and starting to brown. Remove the prosciutto to a paper towel-lined plate, leaving the rendered fat in the pan—this flavorful fat is your sauce foundation.
With the prosciutto fat still in the skillet, reduce the heat to medium-low and add the minced garlic, cooking for just 30 seconds until fragrant—this short time prevents the garlic from burning. Pour in the heavy cream and stir to combine, then add the diced tomato, peas, Italian seasoning, salt, and black pepper. Simmer for 4-5 minutes, stirring occasionally, until the sauce thickens slightly and the peas are heated through. I like to taste and adjust the seasoning at this point—the cream mellows the flavors, so don't be shy with the salt.
Break the cooked prosciutto into bite-sized pieces and add most of it back to the sauce (reserve some for garnish), along with the torn fresh basil. Stir in the fresh lemon juice and red pepper flakes—the acid brightens the rich cream while the heat adds complexity. Drain the pasta and add it directly to the skillet, tossing gently until every strand is coated with the creamy sauce. I find that stirring for 30 seconds helps the pasta absorb the flavors rather than sitting on top.
Divide the pasta among serving bowls, creating a slight well in the center. Top each portion with a generous sprinkle of freshly grated Parmesan cheese and the reserved crispy prosciutto pieces. Serve immediately while the sauce is still creamy and warm.