Begin by preheating a large skillet over medium heat. Slice the day-old baguette into cubes and toss them in olive oil until evenly coated. Add the bread cubes to the skillet and toast for about 5–7 minutes, stirring occasionally, until they turn golden brown and crispy. Remove the croutons and set them aside to cool.

In the same skillet, add a little more olive oil and heat over medium-high. Season the salmon fillets with salt and pepper, then place them in the hot skillet. Cook each fillet for about 3–4 minutes per side, or until the salmon flakes easily with a fork and is cooked through. Transfer the cooked salmon to a plate and allow it to rest before flaking it over your salad.

In a mixing bowl, whisk together the anchovy paste, egg, fresh lemon juice, Dijon mustard, and minced garlic. Blend these ingredients until creamy, then slowly drizzle in vegetable oil while whisking continuously to achieve a smooth consistency. Taste and adjust seasoning with salt or additional lemon juice as needed.

In a large salad bowl, combine the torn romaine lettuce and cooled croutons. Pour the freshly made dressing over the top, tossing gently to coat all the ingredients evenly.

To serve the Salmon Caesar Salad, divide the dressed salad mixture onto individual plates. Flake the reserved salmon fillets on top, then finish with generous shavings of Parmesan cheese.