Preheat your oven to 400°F (200°C). Begin by dicing the baguette into small cubes and place them in a mixing bowl. Drizzle with olive oil and minced garlic, tossing to coat the bread evenly. Spread the cubes on a baking sheet in a single layer. Bake for about 10-12 minutes, or until they are golden brown and crispy, stirring halfway through for even toasting.

While the croutons are baking, heat a skillet over medium-high heat. Lightly grease with olive oil, and season the salmon fillet with salt and pepper. Place the salmon skin-side down in the hot skillet. Sear for 4-5 minutes, then carefully flip and cook for an additional 4-5 minutes, or until the salmon is fully cooked and flakes easily with a fork. Remove from heat and let it rest.

In a medium bowl, combine anchovy paste, a pasteurized egg, fresh lemon juice, and Dijon mustard. Slowly drizzle in vegetable oil while whisking continuously until the mixture becomes creamy and emulsified. Taste and adjust seasoning as needed for your ideal creamy Caesar dressing. Set aside, allowing the flavors to meld together.

In a large bowl, add chopped romaine lettuce along with the freshly baked croutons and grated Parmesan cheese. Gently toss to combine, allowing the ingredients to mix while ensuring the romaine stays crisp. Flake the cooked salmon into large pieces and add it on top of the salad.

Drizzle the homemade Caesar dressing generously over the assembled salad and toss gently to coat all the ingredients. Plate the salad in individual bowls or on a large serving platter. For an elegant touch, garnish with additional Parmesan or croutons. Serve immediately.