Preheat oven to 425 degrees. Place broccoli florets on a foil-lined baking sheet with some olive oil and back for 25 minutes, or until golden, flipping once.
Meanwhile, prepare the rest of your ingredients. In a large baking dish, place potatoes, onions, thyme, nutmeg, sage, garlic, and salt/pepper. Roughly toss together. (Note that using a mandoline such as the one below really helps make slicing potatoes more efficient)
When the broccoli is crispy, place it in a bowl with the heavy cream. Use an immersion blender (alternatively you can use a food processor) and blend until smooth. Add this broccoli cream mixture to the baking dish along with ~¾ cup freshly Parmesan (can use a microplane to finely shred) and about ½ cup water and toss to coat potatoes. Cover dish with aluminium foil.
Turn oven down to 400 degrees and cook potatoes, covered, for 30 minutes. Uncover, top with another ¾ cup shredded Parmesan cheese, and place back in oven, continuing to cook uncovered for another 20-30 minutes or until potatoes are cooked through and crispy on top.