Heat skillet to medium-high heat
Cut butter into 1 tablespoon pieces and add to skillet
Let butter melt until it starts to bubble, then whisk
Add garlic, sage, and salt to butter; continue whisking until the bubbles dissipate and the butter starts to develop brown specks and takes on a nutty aroma
Remove skillet from heat and continue to whisk for 1-2 more minutes while it cools
Add butter to slow cooker along with chicken breasts, broth, and can of diced tomatoes and chilies
Cover and cook on low for 6-8 hours or high for 3-4 hours until chicken is fully cooked
Remove chicken from the slow cooker and shred with two forks
Add heavy cream, spaghetti noodles, and parmesan cheese to slow cooker and press the noodles into the liquid until fully covered and they start to soften
Return chicken to the slow cooker and give everything a stir to combine
Turn slow cooker to high and continue to cook for 30-40 minutes (stirring 2-3 times throughout) until pasta is cooked to al dente
Serve with an extra sprinkle of parmesan cheese and parsley or as desired