1. Preheat oven to 400 degrees. Place the bacon in a single layer on a wire cooling rack atop a baking sheet or on a parchment paper-lined baking sheet. Bake for 20 minutes or until brown and crispy.
2. After about ten minutes, whisk together the eggs, milk, salt, and ground black pepper in a liquid measuring cup or a small bowl. Set aside.
3. Heat a nonstick skillet over medium heat. Butter the inside of all four bagels. Once it is hot, place the bagels cut side down in the skillet and cook for 1-2 minutes or until browned.
4. If needed, wipe the skillet clean with a kitchen or paper towel. Add the butter to the skillet. Once it has melted, swirl the butter around to coat the entire skillet then pour in the egg mixture and cook for 1-2 minutes until the edges are set. Fold half of the egg atop the other half like you would a quesadilla and cook for another 1-2 minutes until cooked through. Remove from heat, slice in half vertically, top each half with two slices of cheddar, and set aside.
5. For the Cholula hollandaise: Add the egg yolks, Cholula, lemon juice, and salt to a blender or use an immersion blender in a deep jar to blend until combined. Use a small saucepan to heat the butter until melted and hot or stick it in the microwave in a liquid measuring cup for one minute. While the blender is running, slowly pour the hot butter in. Once all the butter is incorporated turn off the blender and set aside.
6. To assemble: layer the bottom half of a bagel with a cheesy egg patty, bacon, arugula, and a slice of tomato. Drizzle with Cholula hollandaise then top with the remaining half of the bagel. Serve warm.
- Easy - 25-Minutes