Place the chopped bacon in a 5 QT Dutch oven or large pot and bring to medium heat. Cook, stirring occasionally, until crisp. Transfer the bacon pieces to a stack of paper towels to drain using a slotted spoon. Discard the grease and wipe out the bottom of the pot.
In a small dish, stir together the ½ teaspoon of salt and ¼ teaspoon of pepper with the ¼ cup flour. Place the butter into the pot and bring over medium heat. When the butter is melted, whisk the flour mixture in a little bit at a time until combined. Slowly whisk the milk into the butter/flour mixture a little at a time, until combined and smooth. Add the water and whisk to combine, scraping up any browned bits on the bottom of the pot from cooking the bacon.
Increase the heat to med-high and stir occasionally until boiling. Reduce the heat to med-low and add the macaroni. Cook for 8-10 minutes, stirring regularly to prevent sticking, until pasta is cooked.
While the pasta is cooking, place the broccoli florets into a microwave-safe bowl and cover the bowl with a damp paper towel. Microwave on high for 2 minutes. Broccoli should be softened but still firm and bright green. Set aside.
Once the pasta is cooked, reduce the heat to low and stir in the shredded cheese until melted into the sauce. Add the broccoli florets and the bacon pieces to the pot and stir together until combined. Remove from heat and serve.