Preheat oven to 400°F (204°C).
Halve potatoes lengthwise, poke with a fork several times, and place on a baking sheet.
Bake for 40–45 minutes or until tender; cool slightly.
Scrape potato flesh into a bowl, reserving about 3 cups and discarding excess while keeping skins intact.
Place potato skins back on the baking sheet and set aside.
Melt butter in a medium saucepan over medium heat.
Add olive oil, onion, and broccoli; season with salt and pepper and cook 3–4 minutes.
Add flour and stir until combined; reduce heat to medium-low.
Cook flour mixture for 2 minutes until lightly browned.
Slowly whisk in heavy cream until mixture begins to thicken.
Gradually pour in milk while whisking until sauce coats the back of a spoon.
Season with more salt and pepper if needed.
Stir in cheddar until fully melted, then remove from heat.
Mix cheese sauce with the reserved potato in a large bowl.
Spoon filling into potato skins.
Reduce oven temperature to 350°F (177°C).
Bake filled potatoes for 15 minutes until heated through and lightly golden.