Cook the Pasta & Prep Your Chicken: Get a large pot of water on the boil. Once it’s roaring, salt it generously. Drop in your 1 lb of fettuccine and cook according to package directions, until it’s al dente. CRUCIAL STEP: Before you drain the pasta, use a mug to reserve at least 1 ½ cups of the starchy cooking water. While the pasta cooks, pat your 1.5 lbs of chicken thighs dry and season them liberally on all sides with salt and pepper.
Sear the Chicken to Golden Perfection: Place a large, 12-inch skillet over medium-high heat. Add the 1 tbsp of olive oil and 2 tbsp of butter. Once the butter is melted and sizzling, carefully place the seasoned chicken in the pan in a single layer. Let it cook undisturbed for 3-4 minutes per side until a deep, golden-brown crust forms. Once cooked through to 165°F, remove the chicken from the skillet and set it aside on a plate.
Build Your Flavor Base: Lower the heat to medium. Add the 4 cloves of minced garlic and the 1 finely minced jalapeño to the skillet. Stir them through the leftover drippings for about 30-60 seconds, until fragrant. Pour in the ¼ cup of chicken broth to deglaze the pan. Use a wooden spoon to scrape up all the browned bits from the bottom. Let the broth bubble and reduce by about half.
Create the Silky Cream Sauce: Reduce the heat to low and pour in the 1 ½ cups of heavy cream. Stir everything together and let it come to a gentle simmer. Allow the sauce to bubble softly for 3-4 minutes, stirring occasionally, until it has thickened slightly.
The Grand Finale: Bring It All Together (Off-Heat!): TURN OFF THE HEAT. Remove the skillet from the hot burner entirely. Add the cooked chicken and the drained fettuccine to the sauce. Toss everything to coat. Sprinkle in the 1 cup of freshly grated Parmesan cheese and toss continuously until the cheese is melted. Finally, pour in the juice and zest of 2 limes and the 1 cup of chopped cilantro.
Finish and Serve Immediately: Give it one final toss. If the sauce is too thick, add a splash of your reserved pasta water and stir until it loosens into a luscious sauce. Serve right away, garnished with extra cilantro and Parmesan.