Add the broth and milk to a large pot set over high heat. Bring just to a boil, then reduce to medium-high.: The first aromas you notice will be warm and savory as the broth and milk combine, and a faint steam will rise from the pot. You want the liquid hot enough to dance with small bubbles at the edges, not a furious rolling boil, because intense boiling can make the milk scald and separate. The visual cue to watch for is small steady bubbles and a thin veil of steam, that tells you it is time to reduce the heat to maintain control. If the surface begins to foam aggressively, lower the heat immediately to prevent scorching. A common mistake here is walking away, which risks boiled over liquid or scorched dairy, so stay nearby until you lower the temperature.
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 you add the pasta , you will hear a gentle simmer deepen into a soft bubbling sound. Stirring occasionally prevents the pasta from clumping and encourages even hydration. Watch the edges of the pot for reduced liquid and test a piece of pasta for tenderness; it should be slightly firmer than you want, since it will finish absorbing sauce later. The pasta will look plump and the surface will shine when it is nearly done. Overcooking at this stage can turn the pasta gummy once the sauce finishes, so avoid extended simmering without checking.
Meanwhile, steam the broccoli in the bag (or steam it on the stovetop if using fresh broccoli). Drain the broccoli and cut it up roughly with kitchen scissors.: While the pasta softens, steam the broccoli to preserve its bright color and slightly crisp texture. Steaming in the bag keeps things easy, and you will see a vibrant green color emerge, with a faint vegetal aroma that signals tenderness. If using fresh broccoli , time it so it is just tender when pierced with a fork but not floppy. Drain thoroughly to prevent excess water from diluting the sauce, then chop into bite sized pieces with scissors or a knife. A common pitfall is adding wet broccoli to the pot, which can thin the sauce and cool the mixture too much, so ensure it is well drained.
Turn the heat off and stir the cheese, broccoli, butter, cream cheese, and salt into the pasta mixture. Taste and season with additional salt as needed. Serve.: Once the pot is off the heat, you will feel the residual warmth melt the cheese and cream cheese into a glossy, clinging sauce. Stirring at this stage enhances smoothness and prevents the cheese from seizing up. The aroma shifts to a rich, dairy forward note with green freshness from the broccoli . If the mixture seems slightly loose, letting it sit a minute or two off heat allows the sauce to thicken naturally as the pasta absorbs more liquid. A mistake to avoid is returning the pot to high heat to melt the cheese, which can make it grainy; gentle residual warmth is all you need.
Taste and season with additional salt as needed. Serve: This final moment is all about balance. Sampling a small spoonful will reveal whether the dish needs a little extra salt to bring forward the cheesy notes or if it is already well rounded. The temperature should be comforting warm, with the cheese coating each piece and the broccoli offering brief pops of texture. Serve straight from the pot for an easy family style meal. Avoid over seasoning at this point, since the flavors concentrate slightly as the dish rests; add small increments, taste, and adjust patiently.