Bring a large pot of salted water to a boil and cook the pasta until al dente. Save about ¼ cup of pasta water before draining, as this helps loosen your sauce later. Drain the pasta and set aside.
Heat olive oil in a frying pan over medium-high heat. Add the chicken slices in batches, cooking until lightly golden and nearly cooked through. Remove the chicken and set aside while keeping the pan juices for flavor.
In the same pan, pour in the cream, crumbled stock cube, and a splash of pasta water. Stir and bring to a gentle simmer. Add the pesto and peas, letting everything bubble for a couple of minutes until the peas warm through.
Return the chicken to the pan and stir to coat in the sauce. Add the pasta and Parmesan, mixing until the sauce clings to every piece. Taste and season with salt and pepper as needed.