Make the spicy honey mustard first by combining the mustard, honey, mayo, cayenne pepper, paprika, vinegar, salt, and pepper in a small bowl. Stir until smooth. Taste and adjust the cayenne to your liking. Set aside.
Cut each croissant open and drizzle the cut sides with a little olive oil. Heat a skillet over medium heat and place the croissants cut-side down. Toast until golden brown. Remove and set aside.
In the same skillet, melt the butter over medium-low heat. Whisk the eggs with the milk. Add to the skillet and gently scramble, stirring slowly until just cooked through and still soft. Remove from heat and season with salt and pepper to taste.
Spread the spicy honey mustard generously over each toasted croissant. Divide the scrambled eggs evenly across the four sandwiches, then layer on the brie cheese slices.
Place the open-faced sandwiches into the air fryer at 350 degrees for two minutes or under the broiler in the oven for one minute, just until the brie is fully melted and gooey.
Lay two slices of crispy bacon on each sandwich, close them up, and enjoy right away.