In a large pot with boiling salted water, add in the Broccoli Florets (3 cup) and cook for around 3 minutes to slightly soften the broccoli. Drain and set the broccoli aside.
Place the pot back on the stove over low heat and add in the Butter (2 tablespoon). Move it around to melt. Add in Jalapeño Pepper (2) and let it gently cook for 3-4 minutes over low heat.
Add in the Scallion (2) and leaves from the Fresh Thyme (3 sprig). Stir to sweat down the vegetables.
Add in All-Purpose Flour (2 tablespoon). Stir continuously for another 3 minutes. Then add the Chicken Stock (2 1/2 cup) as you keep stirring. Next, stir in the Milk (2 1/2 cup) and let it come up to a boil. Season with Freshly Ground Black Pepper (1/4 teaspoon) and Salt (1/4 teaspoon).
Add in the Medium Cheddar Cheese (1/3 cup), Aged Cheddar Cheese (1/3 cup) and Pepper Jack Cheese (1/3 cup). Stir well, then add in the broccoli. Let it continue to cook on a rolling boil for 5 minutes. Serve in large bowls and enjoy!