How to Make It
In a large bowl, stir 2 tablespoons of the olive oil with the lemon juice, rosemary and minced garlic. Add the chicken thighs, turn to coat and cover with plastic wrap. Refrigerate for at least 2 hours or overnight.
Preheat the oven to 425°. Wrap the head of garlic in foil, then set on a foil-lined baking sheet and bake for 40 minutes. Arrange the lemon halves cut side down on the baking sheet and bake for 10 minutes more. In a small bowl, toss the bread cubes with 1 tablespoon of the olive oil and spread on the baking sheet; bake until toasted, about 8 minutes. Let the garlic, lemon halves and croutons cool for 5 minutes.
To make the dressing, squeeze the garlic cloves from their skins into a small bowl and mash until smooth. Squeeze the flesh from the roasted lemons into the bowl and add any juices from the baking sheet. Add the remaining 1/2 cup of olive oil, the crème fraîche, cheese and anchovies and stir until smooth. Season with salt and pepper.
Light a grill or heat a grill pan over moderately high heat. Season the chicken thighs with salt and pepper and grill, turning once, until cooked through, 12 to 14 minutes. Transfer the chicken to a plate and let rest for 10 minutes.
To serve, arrange 2 romaine leaves on the bottom half of each toasted bun. Top each with 2 chicken thighs. Spoon the dressing generously over the chicken and then sprinkle the croutons and capers on top. Close the sandwiches and serve immediately with more dressing on the side.