Melt the butter in a medium pot over medium heat. Once foaming, add the diced onion and kosher salt, stirring occasionally for about 5 minutes until the onion becomes translucent and soft. Add the minced garlic and cook for another minute until fragrant. This builds the flavor foundation of the soup—the salt helps draw out the onion's moisture and develop sweetness while the garlic adds depth.

Sprinkle the flour over the aromatic base from Step 1 and stir constantly for 1-2 minutes to cook out the raw flour taste and create a roux. This mixture will thicken the soup and give it a velvety texture. Slowly whisk in the vegetable broth, stirring constantly to avoid lumps. Bring the mixture to a boil, then reduce heat to a simmer—this ensures the flour is fully cooked and the broth is well-incorporated.

Add the chopped broccoli florets to the simmering broth from Step 2. Cook for 8-10 minutes until the broccoli is completely tender and easily pierced with a fork. I like to cut my broccoli into small, uniform pieces so they cook evenly and create a nice texture throughout the soup—not too chunky, not too fine.

Remove the pot from heat and let it cool for about 1 minute. Stir in the whole milk, then add the shredded cheddar cheese in handfuls, stirring gently until completely melted and smooth. The residual heat will melt the cheese perfectly without breaking the soup's emulsion. I find using quality sharp cheddar makes all the difference—it gives the soup a more complex, satisfying cheese flavor without needing extra seasoning. Taste and adjust salt as needed before serving.