How to Make It
In a small skillet, toast the pine nuts over moderate heat until lightly golden, about 4 minutes. Let cool.
In a food processor, combine the pine nuts, arugula, parsley, basil and garlic and pulse until coarsely chopped. Add the mayonnaise, grated cheese, 1 tablespoon of the olive oil and 1 tablespoon of the lemon juice and puree until smooth. Season the aioli with salt and pepper.
Preheat a large griddle. Brush both sides of the bread slices with olive oil and griddle over moderate heat, turning once, until toasted, about 2 minutes. Transfer the toasts to a plate. Add the bacon to the griddle and cook over moderate heat until crisp, 3 to 4 minutes per side; drain on paper towels.
In a medium bowl, gently toss the tomato slices and torn frisée with 1 tablespoon of the olive oil and the remaining 1/2 tablespoon of lemon juice; season with salt and pepper.
In a large nonstick skillet, heat the remaining 2 tablespoons of oil. Crack the eggs into the skillet and fry sunny-side up or over-easy. Transfer to a plate and season with salt and pepper.
Lay 6 slices of toast on a work surface and spread with the aioli. Top with the tomatoes and frisée, then the bacon and eggs. Close the sandwiches, cut in half and serve right away.