For the crispy shallots: Place the shallots and oil to cover in a small pot. Turn heat to medium-high and cook until the shallots are slightly brown and beginning to crisp, 15 to 20 minutes. Remove the shallots with a slotted spoon or spider and transfer to a paper towel lined plate to crisp (reserve the oil and let cool; oil keeps for about a week and makes a great flavored oil).
For the Brussels sprouts: Preheat the oven to 450 degrees F.
Place the Brussels sprouts in an even layer in a large cast-iron pan. Drizzle with olive oil to coat. Season with salt and pepper and toss. Lay Brussels sprouts cut-side down in an even layer. Roast until golden brown, 20 to 25 minutes.
Add roasted Brussels sprouts, vinegar, neonata and salt to taste in a large bowl. Toss to combine.
Mix creme fraiche and 1 tablespoon olive oil in a small bowl until smooth and combined.
Transfer the Brussels sprouts to a platter. Top with dollops of the creme fraiche and the frizzled shallots. Serve!