Bring a large pot of salted water to a rolling boil, then add the pasta and cook until just al dente, about 8-10 minutes. Drain and set aside, reserving a cup of pasta water.
While the pasta cooks, heat a large skillet over medium-high heat. Add a tablespoon of olive oil, then carefully place the shrimp in the pan. Sear for 2-3 minutes per side until they turn pink and develop a slight char, filling the kitchen with a warm, savory aroma. Remove the shrimp from the pan and set aside.
Lower the heat to medium and add another tablespoon of olive oil to the same skillet. Sauté the minced garlic until it becomes fragrant, about 30 seconds, being careful not to burn it. Then, stir in the adobo sauce with chipotle peppers, cooking briefly to deepen the smoky flavor.
Pour in the heavy cream, stirring well to combine with the smoky garlic mixture. Let it simmer gently for 2-3 minutes until it starts to thicken slightly and fills the kitchen with a rich, smoky scent. Season with salt and pepper to taste.
Return the cooked shrimp to the skillet, stirring to coat them evenly in the sauce. Add the drained pasta to the pan, tossing everything together until the noodles are fully coated and the sauce clings beautifully. If the sauce is too thick, loosen it with a splash of the reserved pasta water, stirring gently.
Turn off the heat and sprinkle the grated Parmesan cheese over the pasta. Stir until the cheese melts into the sauce, creating a glossy, velvety coating. Taste and adjust seasoning as needed.
Let the pasta rest for a minute off the heat to allow the flavors to meld. Serve immediately, garnished with extra cheese or herbs if desired, and enjoy the smoky, spicy richness of this twist on classic carbonara.