Season chicken breasts all over with kosher salt and black pepper.

Heat 1 tablespoon of olive oil in a large pot or Dutch oven over medium heat until shimmering. Add the chicken and spread into an even layer. Cook until browned on both sides and cooked through, 4 to 5 minutes per side. Transfer to a plate.

Reduce the heat to low. Add 2 tablespoons of unsalted butter to the pot and let it melt while scraping up the browned bits from the bottom of the pot with a wooden spoon.

Add minced garlic cloves and minced shallot. Cook, stirring occasionally, until fragrant, about 2 minutes.

Stir in chicken broth and heavy cream, scraping up any remaining bits from the bottom of the pot. Increase heat to medium.

Add dried fettuccine pasta and remaining 1 tablespoon of olive oil. Bring to a simmer and cook, stirring often and scraping against the bottom and corners of the pot, until pasta is al dente and sauce is reduced by about half, 15 to 20 minutes.

Add grated Parmesan cheese and chipotle in adobo sauce to the pot, and toss with tongs until well-combined and the cheese is melted, about 3 minutes.

Return the chicken and any accumulated juices on the plate to the pot. Continue to cook, tossing occasionally, until the sauce is thickened slightly and coats the pasta well, about 3 minutes.

Taste and season with more kosher salt and chipotle in adobo sauce as needed. Serve topped with more grated Parmesan if desired.