First, add chicken breasts to a medium pot, season with kosher salt & black pepper and cover with at least 1" of water. Bring up to a boil, then cover with a lid, reduce heat to low and let simmer for about 10-15 minutes, or until the internal temperature reaches 165F. Timing will vary depending on how large/thick your chicken breasts are.
1 lb boneless, skinless chicken breast
Next, transfer cooked chicken to a large bowl, or the bowl of a stand mixer, and shred it. Alternatively, you can use 2 forks to shred it, but I like the mixer method because it's quicker! You can also substitute about 2.5 cups of shredded rotisserie chicken.
Bring a large, high-sided pan up to medium heat and add oil or butter. Then, add diced onion and season with kosher salt. Sauté, stirring occasionally, for 5 minutes, until softened. Stir in the garlic and smoked paprika and cook for another 30 seconds, until fragrant. Add in the flour and stir until everything is coated. Allow the flour to cook off for 1 minute.
1 tbsp olive oil, ½ large yellow onion, 4 large garlic cloves, ½ tsp smoked paprika, 3 tbsp AP flour, 2 tbsp butter
Gradually add in the broth, stirring well after each addition. Repeat with the milk. Season with dijon mustard, a dash of cayenne pepper, and a generous amount of kosher salt & black pepper, then bring up to a gentle boil.
1 ½ cups chicken bone broth, 2 cups whole milk, 1 tbsp dijon mustard, kosher salt & black pepper, cayenne
Next, add in the broccoli florets and carrots, making sure they're submerged by liquid. Reduce heat to a simmer (about medium-low to low) and cook for 5 minutes. Stir in the gnocchi and continue simmering for 4-5 more minutes, until tender.
10 oz finely chopped broccoli florets, ½ cup grated or matchstick carrots, 1 package potato gnocchi
Stir in the shredded chicken until incorporated, then remove the pan from the heat and add the shredded cheddar in batches, stirring well after each. Taste and adjust the amount of kosher salt & black pepper to taste -- don't be shy here! I recommend allowing it to cool for at least 5 minutes, as this will help the sauce thicken up. Enjoy!
8 oz extra sharp yellow cheddar cheese