Bring a large pot of salted water to a rolling boil. Add pasta and cook until 1 minute shy of al dente (check package time, subtract 1 minute). Reserve ½ cup pasta water before draining. Drain pasta and set aside.

While pasta cooks, pat chicken dry with paper towels. Slice each breast horizontally into two even cutlets (about ½-inch thick). Season both sides with ½ teaspoon salt and ¼ teaspoon pepper.

Heat olive oil in a 12-inch heavy skillet over medium-high heat until shimmering. Lay chicken cutlets in a single layer (work in batches if needed). Cook 3-4 minutes per side until golden brown and internal temperature reaches 165°F. Transfer to a plate and tent loosely with foil.

Reduce heat to medium. Add sliced garlic to the skillet and cook 30 seconds until fragrant, scraping up any browned bits. Pour in chicken broth and bring to a simmer, stirring constantly to deglaze the pan.

Whisk in heavy cream (or coconut milk) and pesto until smooth. Simmer 1-2 minutes until slightly thickened. Taste and add remaining ½ teaspoon salt and ¼ teaspoon pepper if needed.

Add drained pasta and ¼ cup reserved pasta water to the skillet. Toss with tongs over medium heat for 1-2 minutes until the sauce coats each piece of pasta. If too thick, add remaining pasta water a tablespoon at a time.

Slice the rested chicken across the grain into ½-inch strips. Add chicken and any accumulated juices back to the skillet. Toss gently to combine. Remove from heat.

Serve immediately, topped with grated Parmesan, pine nuts, and fresh basil if using. Leftovers keep in an airtight container in the fridge for up to 3 days.