Cook and drain bacon and reserve. The easiest way to cook bacon is on baking sheets with parchment paper in the oven.
Slice the jack. Butter what will become the outside of the sandwiches on all slices of bread.
Arrange jack on bread slices, cover half with crispy bacon and close sandwiches by placing the tops and bottoms together.
Heat a skillet over medium heat and grill the sandwiches 3-5 minutes, until golden brown on the first side, then flip and repeat on second side.
Remove from skillet, and pry sandwiches open, slice avocados and fan out avocado slices into sandwich, then carefully reclose sandwiches and cut in half and serve.
For the Grainy Dijon Beer Sauce
Sauté onion by slowly cooking it in butter, stirring occasionally for 3-4 minutes. Add garlic into butter and sauté further until softened and pungency has been cooked out.
Add flour to the pot and mix thoroughly, then toast the flour mixture for a minute or two while stirring occasionally.
The first addition of liquid will be the beer, add the beer and stir into the onion, butter and flour and then drizzle in milk bit by bit mixing vigorously between additions.
Add the Dijon mustard. Season with a pinch of salt and optionally white pepper and ground nutmeg. Taste and adjust seasoning as needed.