Preheat the oven to 400°F. Place potatoes directly on the oven rack (or on a baking sheet) and bake for 1 hour, until tender.
Remove from the oven and let cool for about 10 minutes, until easy to handle.
Slice the potatoes in half lengthwise. Carefully scoop out the flesh into a mixing bowl, leaving a thin layer inside the skins to keep them sturdy.
Mash the potato flesh with the butter, sour cream, salt, and milk until smooth. Stir in the broccoli and cheddar cheese.
Spoon the mixture back into the potato skins, dividing evenly.
Place the filled potatoes on a baking sheet and return to the oven. Bake for 10 minutes, until heated through and the tops are lightly golden.
Serve warm.
Notes
Don't overmix the filling. This creates gluey mashed potatoes instead of light and fluffy.Make Ahead: You can prep these twice baked potatoes up to the filling step (don't do the second bake) a day in advance. After stuffing the potato skins, just cover them tightly and refrigerate until you're ready to bake!To Freeze: Assemble the potatoes through the filling step and let them cool completely. Flash freeze them on a baking sheet until solid, then transfer to a freezer-safe bag or container. When you're ready to serve, bake straight from frozen at 375°F for 25-30 minutes, until heated through and the tops are golden and melty.