Add potatoes to a large pot. Cover with water, and add a tablespoon of salt. Place the pot over high heat and bring to a boil. Reduce heat to medium-low and allow potatoes to cook until fork tender. about 20-25 minutes. Drain potatoes and return to the pot.
Remove stems from broccoli and discard. Finely chop the remaining florets.
Combine potatoes, broccoli, cheddar cheese, butter, and sour cream in your cooking pot using a hand mixer.
Beat until the mashed potatoes are your desired consistency - smooth or a little lumpy. Taste and season with salt and pepper as needed. Serve warm.
Notes
If you prefer, you can mix the potatoes, broccoli, cheese, butter, and sour cream in the bowl of your stand mixers, Use the paddle attachment on medium-low speed until the potatoes reach your desired smoothness.