Preheat the oven to 425F and start boiling a pot of water.
Melt the butter in a skillet over high heat and saute the onions and leeks with salt until they’ve started to brown. You may need to add an additional teaspoon of canola oil to the skillet. Remove from the skillet and set aside to cool.
Boil the potatoes until just cooked through, 10-15 minutes. Add the broccoli crown to the pot at the start, stem side down. Remove the broccoli after 6 minutes and put it into an ice bath.
Trim the broccoli florets and return any remaining stem to the pot to finish cooking with the potatoes.
Drain the potatoes and broccoli stem, putting the broccoli stem into the ice bath with the florets. Leave the potatoes in a colander and refrigerate until needed.
Remove the broccoli from its ice bath and chop finely, into about ¼ inch dice. Chop gently so as not to mash them.
Transfer the potatoes to a mixing bowl and use a whisk to smash the potatoes. They should not be mashed, but smashed with numerous approximately ½ inch chunks remaining. If using a regular potato masher, be careful to meet this criteria.
Add the broccoli, leek-onion mixture, manchego cheese, and half cup of parmesan to the potatoes.
In a separate mixing bowl, add the eggs and whisk them to combine. Add in the sour cream, heavy cream, black pepper and garlic and whisk until well mixed. Add to the vegetable and cheese mixture and use a spatula to gently stir to combine. Be gentle to not mash the vegetables.
Grease a muffin tin and add ⅓ cup of the potato-egg mixture to each tin. Sprinkle the last half cup of parmesan on top of each cup. Press the mixture with your fingers until it is mostly flat on top. Bake for 20-25 minutes, until the parmesan on top is starting to brown.
Loosen the medallions in the muffin tin by running a butter knife around the sides and turn the tin upside down over a greased baking sheet. Strongly tap the muffin tin cups to free the medallions.
Bake the medallions for another 15 minutes, or until the tops are brown and crispy.
Optional: Broil for 2 minutes on high to get extra crispy tops