Make cloud bread: separate eggs, beat whites to stiff peaks with cream of tartar. Fold in softened cream cheese and yolks. Bake at 150°C for 25 minutes until golden.
Prepare béchamel: melt butter in small saucepan, whisk in almond flour, cook 1 minute. Slowly add cream, whisking constantly until thick. Season with nutmeg, salt, pepper.
Preheat grill/broiler. Spread Dijon on two cloud bread slices. Layer with ham and half the Gruyère.
Spread béchamel over top. Sprinkle remaining Gruyère. Grill 3–4 minutes until golden and bubbling.
Meanwhile, fry eggs in butter to your liking. Season.
Top each croque with a fried egg. Serve immediately with a simple green salad.