In a 12-in (30-cm) oven-safe skillet, add the olive oil over medium heat. Once the oil begins to shimmer, add the Brussels sprouts and cook, stirring occasionally, until crisp and lightly caramelized, 3 to 4 minutes.
Add the garlic, ginger, and lemon zest. Cook until fragrant about 30 seconds.
Transfer the skillet to the oven and roast for 10 minutes, or until tender. Remove from the oven.
Preheat oven to broil.
In a blender or food processor, add the goat’s milk, goat cheese, mustard, and lemon juice, and pulse until smooth. Stir in the red pepper flakes.
Add the basil to the skillet with the Brussels sprouts. Add the goat’s milk mixture and stir to combine.
Sprinkle with Parmesan cheese and almonds.
Broil for 2 to 3 minutes, or until the cheese has melted.
Season with salt and pepper, and top with additional basil.