Preheat a grill to medium heat or heat a grill pan on the stovetop.
Rub the chicken breasts with 1/2 tablespoon of the olive oil. Season both sides with 1/4 teaspoon kosher salt, 1/4 teaspoon ground black pepper, 1 teaspoon garlic powder, 1/2 teaspoon paprika, and 1 teaspoon dried oregano.
Grill the chicken until an instant-read thermometer inserted into the thickest part reads 165°F, about 8–10 minutes per side. Transfer to a cutting board and let rest 10 minutes, then slice.
Brush or drizzle the cut sides of the baguette with remaining olive oil. Grill the baguette cut-side down and the lemon halves cut-side down until charred, about 2–3 minutes. Transfer the baguette to a board and rub the interior with the garlic clove.
Squeeze about 2 tablespoons juice from the grilled lemon into a small bowl. Whisk in the mayonnaise, Dijon mustard, and anchovy paste. Gradually whisk in the remaining 2 tablespoons olive oil until combined, then stir in 1/4 cup grated Parmesan.
In a large bowl, toss the chopped romaine and finely chopped celery with 1/4 cup of the dressing and 1/4 cup grated Parmesan until evenly coated.
Spread remaining dressing onto the grilled baguette, then layer with sliced grilled chicken, the romaine-celery salad, and sliced tomatoes. Sprinkle with shaved Parmesan, cut each sandwich in half to create four sandwiches, and serve.