In a large pot bring some water to boil, add salt. Pour broccoli in and blanch for 2 minutes. Drain and rinse with cold water and set aside.

Put pot back on stove, add 2 tablespoons butter and chopped onion. Sauté until translucent then stir in garlic for about 30 seconds to a minute.

Push onion and garlic to the side of the pot and add remaining 2 tablespoons of butter and flour to the middle of the pot. Whisk for 2 minutes the flour and butter mixture.

Add 2 cups chicken stock and 2 cups half and half and bring to a simmer for 20 minutes. Do not boil.

Add shredded pepper jack cheese a little at a time and stir while it melts. Once cheese is melted add broccoli. Stir for 10 minutes then serve.