Scrub potatoes clean and dry thoroughly. Pierce each potato several times with a fork. Rub lightly with oil and salt, then bake directly on the oven rack or on a baking sheet until tender and crisp-skinned.

Steam or microwave broccoli just until tender-crisp. Drain well and chop into bite-sized pieces.

In a bowl, combine butter, warm milk or cream, and shredded cheese. Stir until smooth and creamy.

Slice each baked potato lengthwise and gently fluff the interior with a fork, keeping the skin intact.

Spoon cheese mixture into the potato, then fold in broccoli. Add more cheese on top if desired.

Return filled potatoes to the oven briefly until cheese is melted and bubbly. Serve hot.