Preheat your oven to 400°F (200°C). Wash the potatoes thoroughly and pat them dry.
Pierce each potato several times with a fork and rub with a little olive oil. Place directly on the middle oven rack.
Bake for 45-60 minutes, or until you can easily pierce them with a fork.
While the potatoes are baking, steam the broccoli florets until tender-crisp, about 4-5 minutes.
Once the potatoes are done, let them cool for 10 minutes. Cut them in half lengthwise.
Carefully scoop out the potato flesh, leaving about 1/4 inch around the skins to maintain structure.
In a large bowl, mash the potato flesh with butter, sour cream, and milk until smooth.
Fold in 1 1/2 cups of cheese, steamed broccoli, garlic, salt, and pepper.
Spoon the mixture back into the potato skins and top with remaining cheese.
Return to the oven for 15-20 minutes, until the cheese is melted and golden.