To prep the dipping ingredients: Preheat the oven to 400 degrees F. Line a baking sheet with parchment, spread out the florets of broccoli, wedges of squash and green onions. Drizzle with a bit of olive oil and toss them together. Sprinkle with salt and pepper. Transfer to the oven and roast for 10 to 15 minutes. Remove the broccoli and green onions; return the baking sheet back to the oven to roast the squash for a remaining 10 to 15 minutes, until tender. Turn the heat down to 200 and add all of the veggies back to the baking sheet and transfer back to the oven to keep warm.
Meanwhile, to a medium sauté pan, over medium heat, add a tablespoon of oil. When hot, add Brussels sprouts, cut side down to the pan. Sear for 1 to 2 minutes, until crispy and browned. Remove from the pan and transfer to the baking sheet with the rest of the veggies.
To make the cheese sauce: In a bowl, toss the gruyere and manchego with the flour and a squeeze of lemon juice. Pour the prosecco into the fondue pot, placed over medium high heat. When the prosecco is warm, add the cheese, mustard, salt, pepper and nutmeg. Stir until smooth. Bring to a simmer and continue to stir, it will thicken as it heats up.
Transfer all of the veggies and slices of apple to a serving platter and serve alongside the fondue pot!