Ingredients
For the Sandwich
- Sliced sourdough bread (whole wheat, good quality)
- Swiss cheese, sliced (½ lb)
- Cooked ham, thinly sliced (preferably prosciutto cotto, or mild cooked ham)
- Gruyère cheese, grated
- Eggs (4)
- Dijon mustard
- Butter (for griddling)
For the Béchamel
- Butter (3 Tbsp)
- All-purpose flour (3 Tbsp)
- Whole milk, warmed (2 cups)
- Tabasco
- Nutmeg
- Salt and pepper
Instructions
Prepare the Béchamel
- Warm the milk in the microwave until hot (this prevents lumps when added to the roux).
- Melt 3 Tbsp of butter in a small saucepan over medium-low heat.
- Add 3 Tbsp of flour in equal quantities to the butter, stirring to combine with no lumps.
- Cook the roux over medium-low heat until it develops a honeycomb texture and bubbles (about 2 minutes). This signals the flour is cooking.
- Slowly add the warm milk to the roux while whisking constantly to prevent lumps. The mixture will thicken immediately.
- Bring the mixture up to a simmer, continuing to whisk. This activates the starches and reaches full thickening potential.
- Remove from heat and season with salt, a dash of Tabasco, a pinch of nutmeg, and white pepper to taste.
- Transfer the béchamel to a separate bowl and let it cool, stirring occasionally. (Can be made ahead and used from the fridge.)
Assemble the Sandwiches
- Spread a thin layer of Dijon mustard on all eight bread slices for full coverage. This adds crucial acidity and spiciness to balance the richness.
- Top each bread slice with a light layer of cooled béchamel, spreading it gently.
- Layer sliced Swiss cheese on all slices. The cheese on both top and bottom acts as glue to hold the sandwich together.
- Layer thinly sliced cooked ham on top of the cheese.
- Close the sandwiches by pairing the bread slices together. Set aside.
Cook the Eggs
- Preheat your griddle across two burners on medium-medium high heat.
- Add 1 Tbsp of butter to the griddle and let it melt.
- Crack the four eggs onto the griddle, breaking the yolks and spreading them around so the yolk distributes throughout the egg.
- Season the eggs with salt and pepper.
- Cook over medium heat until the yolks are just slightly set (still orange, not fully opaque).
- Transfer each cooked egg onto the bread of a sandwich, placing it in the center. The egg will be insulated by other ingredients.
Griddle the Sandwiches
- Close the sandwiches with the egg inside.
- Spread a thin layer of the remaining 4 Tbsp of unsalted butter on the first side of the bread (these sandwiches already contain plenty of fat).
- Place the sandwiches on the griddle, buttered side down, on medium heat.
- Use a press to weigh them down for even contact with the griddle. This ensures golden brown crust and fuses all layers together.
- Cook until the first side is golden brown and the cheese on the lower bread is melted.
- Spread butter on the second side of the bread.
- Flip the sandwiches and cook the second side until golden brown and crispy.
Broil and Finish
- Preheat your oven broiler before you start gridding the sandwiches.
- Once the sandwiches are golden on both sides, top each with a generous layer of béchamel, leaving a bit of space around the edges (it will spread under the broiler).
- Top with grated Gruyère cheese (about 2 oz per sandwich).
- Turn off the griddle heat to prevent carryover cooking on the bottom.
- Transfer the griddle to the oven and broil until the tops are bubbly and browned (about 3 minutes). Watch closely to prevent burning.
- Remove from the oven and let cool for a moment before serving.
- Serve with a knife and fork—this is a very gooey sandwich!