Set a pot of water to boil to cook the fettuccine pasta and cook the pasta to al dente while you prepare the rest of the recipe.
In a large, high-walled skillet, heat 1/2 tbsp of olive oil over medium-high heat. Add the chicken pieces, season the chicken with salt and pepper, and cook the chicken until cooked through. Remove the cooked chicken to bowl.
Add the other 1/2 tbsp of oil to the skillet along with the asparagus pieces. Cook the asparagus until crisp-tender and then remove the asparagus to the bowl with the chicken.
Carefully wipe out the skillet if necessary. Add the butter and melt over medium heat. Then add the garlic and cook until fragrant, about 1 minute.
Add the half & half and the softened cream cheese. Stir until the cream cheese is completely melted and smooth. Season with a little salt and pepper.
Now add the grated Parmesan cheese and the pesto sauce. Whisk to incorporate and then let the sauce gently simmer for a few minutes until the cheese has melted and the sauce has slightly thickened.
Add the chicken and asparagus back to the skillet and toss to coat in the sauce. Then add the cooked fettuccine to the skillet and toss to coat the pasta in the sauce. Add some of the starchy pasta cooking water to loosen the sauce if necessary. The sauce will continue to thicken upon standing.
Remove the skillet from the heat and top with a little extra Parmesan cheese to serve. Enjoy!
Store leftovers in an air-tight container in the refrigerator for up to 3 days. To reheat, add a little milk or half & half into the bowl with the pasta and microwave until warm.