Preheat oven to 350°F (175°C).
In a bowl, mix the cream cheese, sugar, and lemon juice until smooth and creamy.
Using a sharp knife, make 4 shallow slits across the top of each bagel—don’t cut all the way through. These cuts are where the garlic sauce and cream cheese will settle in.
Fill the slits generously with the cream cheese filling. I like to chill the filled bagels for a few more minutes before dipping to help the filling set.
In a bowl, whisk together the melted butter, garlic, sugar, egg, milk, mayo, and parsley until smooth.
Dunk the top of each stuffed bagel into the garlic sauce and place them on a parchment-lined baking tray.
Bake for 10–15 minutes in the preheated oven until golden brown and the tops are slightly crisp.
These are best served warm when the outside is toasty and the inside is gooey and rich.