Pound the chicken breasts to an even thickness of about 1/2 inch if needed. In a bowl, combine 2 tbsp olive oil, 1.5 tbsp adobo seasoning, 1 tsp achiote paste (optional), 3/4 tsp kosher salt and 1/2 tsp black pepper. Rub the mixture evenly over both sides of the chicken. Cover and let marinate at room temperature for 15 minutes or refrigerate for up to 2 hours.

Grill or pan-sear

Preheat a grill or heavy skillet over medium-high heat and brush the grates or pan with a little oil. Grill the chicken 4–6 minutes per side (depending on thickness) until the internal temperature reaches 165°F (74°C) and the exterior is nicely charred. If using a skillet, cook 4–5 minutes per side. Transfer to a cutting board and let rest for 5 minutes.

Slice

Slice the rested chicken thinly on the bias into strips about 1/4-inch thick. Keep warm while assembling the salad.

Caesar Dressing

In a medium bowl, whisk together 1/4 cup mayonnaise, minced anchovy fillets (or anchovy paste), minced garlic, 1 tsp Dijon mustard, 1 tsp Worcestershire sauce and 2 tbsp fresh lemon juice until smooth.

While whisking constantly, slowly drizzle in 1/2 cup extra-virgin olive oil to emulsify the dressing. Once combined, whisk in 1/4 cup finely grated Parmigiano-Reggiano. Season with 1/4 tsp freshly ground black pepper and about 1/4 tsp salt; adjust lemon, salt or anchovy to taste for brightness and umami.

If the dressing is too thick, whisk in a teaspoon of warm water at a time until it reaches a creamy, pourable consistency. Refrigerate the dressing up to 24 hours; bring to room temperature and whisk before using.

Salad Assembly

Toss the chopped romaine (6 cups) in a large bowl with about 3/4 of the dressing (start with 3–4 tbsp and add more to taste) until the leaves are evenly coated but not soggy.

Add 1.5 cups croutons and 3/4 cup finely grated Parmigiano-Reggiano to the dressed lettuce and gently toss to combine.

Top the salad with the sliced grilled adobo chicken, arranging the strips evenly across the greens.

Finish with additional Parmigiano-Reggiano shavings, a grind of black pepper and lemon wedges at the side. Serve immediately.