Add the broth and milk to a large pot set over high heat. Bring just to a boil, then reduce to medium-high.: You will notice steam rising and the aroma of warm milk and broth mingling, a sign the liquid is nearing the right temperature. The brief rapid bubble at the start helps kick the cooking process, but you want to lower to medium-high so the liquid simmers steadily, not vigorously boil. This gentler simmer protects the texture of the milk and prevents scorching at the bottom. A common mistake is keeping the pot at full boil, which can lead to curdling or scorching, so reduce the heat as soon as it bubbles.
Stir in the pasta and salt, and simmer for 10-12 minutes, stirring occasionally or until the pasta is just soft. (The liquid will not be totally absorbed and that is okay—it will be by the end of the process!): As the pasta hits the warm liquid, you will hear a soft bubbling and see tiny foam rings form, signaling starch release. Stirring every few minutes prevents the pieces from clumping and ensures an even cook. The salt in the water seasons the pasta from within, which makes each bite more flavorful. Watch the texture closely near the lower end of the time window, and test a piece so it is tender but still has a little bite. Overcooking can produce mushy texture, while undercooking leaves the center chalky.
Meanwhile, steam or otherwise warm the broccoli or peas if using. Drain. Cut up the broccoli, if using.: Warming the frozen broccoli or peas first makes sure they retain color and texture once combined. Steaming preserves bright green hues and gives a clean vegetal scent, whereas boiling can soften them too much. After steaming, drain well so extra water does not dilute the sauce. If using broccoli florets, cut them to bite size so every forkful has a good balance. A slip here is adding vegetables straight from frozen without draining, which can water down the final sauce.
Turn the heat off under the pasta and stir the cheese, broccoli, butter, cream cheese, and salt into the mixture. Taste and season with additional salt as needed. Serve.: With the pot off the heat, the residual warmth is perfect to melt the cheddar cheese and cream cheese into a silky emulsion. You will see glossy ribbons form as the cheeses soften into the liquid, and the aroma of melted cheddar cheese will bloom. Adding the butter at this stage enriches the mouthfeel, and folding in the prepped broccoli or peas keeps them vibrant. Taste carefully before adding more salt , because the cheeses can contribute saltiness. A typical error is returning the pot to high heat to melt the cheese, which can separate the fats and make the sauce grainy, so keep it off heat and stir gently.
Serve.: The final sensory cue is the way the glossy sauce clings to each piece of pasta , and how the steam carries the blended aromas of cheddar cheese and butter. Spoon portions into bowls so each serving has a balance of pasta and vegetables. Let the dish rest a minute to settle; this short pause allows the sauce to thicken slightly. Avoid covering hot containers tightly right away because trapped steam can make the pasta overly soft.