I used this recipe from Pioneer Woman (who I am recently obsessed with), and just altered it to what I had.
1 whole onion, diced
1 stick (1/2 c.) butter
1/3 c. flour
4 c. (1 qt.) whole milk
2 c. half and half
4 heads broccoli cut into florets
1 pinch nutmeg
3 c. grated cheese (mild cheddar, sharp cheddar, jack, etc.)
Dash of salt
Freshly ground black pepper
Smidgen of chicken broth if needed for thinning
1. Melt the stick of butter and then add all of the onion, cooking 2-3 minutes until onions are translucent.
2. Sprinkle flour over the melted butter and onions. Stir to combine, and cook for 1 minute or so. This is called a roux.
3. Pour in milk and half and half. Stir.
4. Add nutmeg, **then broccoli, a small dash of salt, and plenty of black pepper.
**I accidentally cooked my broccoli first because I am made of straw.
Cover and reduce heat to low. Simmer for 20 to 30 minutes, or until the broccoli is tender. IF you cook the broccoli first like I did, just simmer for a few minutes. You don't want the broccoli to get mushy.
5. Find an adorable gal to help add the cheese. (3 cups is one and a half bags). Stir and allow to melt.
Taste seasonings and adjust if needed. Serve it up chunky, mash it up with a potato masher to break it up a bit, or pour in a blender in two batches and puree completely. (If you puree in a blender, return it to the heat and allow to heat up. Splash in chicken broth if needed for thinning.)