You need small springform pans for this recipe to work and look the way it does in the photo.
Use the recipe for cakey cookies linked above but with only 50% of the chocolate chips. Bake half the cookies the regular way, and the other half in the mini springform pans.
Melt the butter in a frying pan and whisk in the flour. Cook about 2 minutes until the flour is fully incorporated. Whisk in the milk and bring to a simmer. Add a little more milk if needed if the sauce is too thick, or alternatively, cook a little longer if it is too thin. Season well with salt.
Form the burgers the same shape and size as the cookies and season with salt and pepper. Cook in a hot pan to brown on both sides and cook to desired doneness.
Build the burger with the bottom bun first, then the burger, then the bacon, then the sauce, then the top bun.