Melt butter in a pot over medium heat and add garlic. Cook for about two minutes.

Whisk in the flour, then slowly add the broth, whisking between each addition to prevent lumps. Stir in the half and half, water, broccoli, and penne noodles and bring to a boil at medium high heat.

Once it begins boiling reduce the heat to medium and let it simmer, stirring occasionally, until the broccoli and noodles are tender, about 12-15 minutes.

Remove from heat and stir in the cheese until melted and smooth.