Bring a pot of salted water to a boil and cook pasta until al dente. Reserve 1 cup pasta cooking water before draining.
While pasta cooks, heat oil in a large high-sided skillet over medium-high heat. Season chicken (or shrimp) evenly with 1/2 tsp. salt and 1/2 tsp. black pepper. Add to skillet, and cook 6 to 7 minutes, turning to brown all sides, until cooked through (shrimp will only need 3 to 4 minutes total). Transfer to a plate.
Add pancetta and shallots to pan; cook 3 minutes, until pancetta is crispy and shallots are soft. Add sun-dried tomatoes and garlic; cook 1 more minute. Add spinach and cook until wilted, about 1 more minute. Add chicken back to pan, and reduce heat to medium-low.
To a blender, add cream cheese, cashew milk, Parmesan, 1/2 cup of reserved pasta cooking water, and remaining 1/2 tsp. salt and 1/2 tsp. black pepper; blend until smooth. Pour sauce into skillet with pancetta and vegetables. Add cooked pasta and toss to combine. Cook for 2 more minutes, stirring frequently, until sauce thickens and begins clinging to noodles. Stream in more pasta cooking water as needed.
Garnish with parsley or basil and extra Parmesan cheese.