Season the chicken: Pat chicken dry and season both sides with salt and pepper.
If you like, add a pinch of red pepper flakes.
Layer the base: Add chicken to the crockpot. Pour in the chicken broth and half of the pesto. Scatter in the minced garlic if using.
Cook low and slow: Cover and cook on Low for 3.5–4.5 hours or on High for 2–3 hours, until the chicken is cooked through and easily shreds.
Aim for an internal temp of 165°F.
Boil the pasta: About 15 minutes before the chicken is done, cook pasta in salted boiling water until just shy of al dente. Reserve 1/2 cup pasta water, then drain.
Shred the chicken: Transfer chicken to a cutting board and shred with two forks. Return it to the crockpot.
Make it saucy: Stir in the remaining pesto, Parmesan, and cream (start with 1/2 cup).
Add butter or a drizzle of olive oil for extra richness. Taste and adjust salt and pepper.
Add pasta and veggies: Stir in the cooked pasta. If using spinach, add it now so it wilts.
For tomatoes or broccoli, fold them in gently. If the sauce seems thick, loosen with a splash of pasta water.
Brighten and finish: Add lemon zest and a squeeze of lemon juice. Taste again and adjust seasoning.
Let everything warm together on Low for 5–10 minutes.
Serve: Top with extra Parmesan and a crack of black pepper. A drizzle of good olive oil is a nice touch.