Trim the stem of each Brussels sprout and cut in half if larger than ½-inch diameter. Drizzle trimmed and cut sprouts with oil and sprinkle with salt and pepper. Toss to coat and pour onto a baking sheet in an even layer. Roast in the preheated oven until tender-crisp, 12-15 minutes. A knife inserted will meet a little resistance. Remove from the oven.
While roasting, cook bacon in a large skillet over medium-high heat. Transfer cooked bacon to a towel-lined pan. When all bacon is cooked, leave bacon grease in skillet and remove from heat if the Brussels have not finished roasting.
Transfer half of the roasted Brussels sprouts to the hot skillet. Fry the sprouts until crispy and browned, 3-5 minutes. Transfer to a towel-lined tray and continue frying the second batch of sprouts. If skillet seems dry, add 2 tablespoons of neutral oil. Finish frying sprouts and transfer to a serving plate.
For the aioli
In a large measuring glass, combine the egg, mustard, lemon zest, lemon juice, salt, pepper, and garlic cloves.
Using an immersion blender, food processor, or standard blender, blend the ingredients until combined.
With blender running, slowly pour in oil until the consistency is thick and white, 1-2 minutes.
Taste for seasonings and set aside in refrigerator until ready to use.