Step 1

Whisk mustard, Worcestershire, garlic, 2 Tbsp. lemon juice, and 2 tsp. black pepper in a medium bowl. Whisking constantly, stream in ⅓ cup oil until emulsified. Transfer half of marinade to a small bowl, then whisk in mayonnaise and cornichons (this will be the special sauce). Season mayo dressing with salt; set aside.

Step 2

Season chicken thighs with salt and add to medium bowl with remaining marinade. Toss to coat. Let sit at room temperature, tossing occasionally, at least 30 minutes, or chill up to 4 hours.

Step 3

Prepare a grill for medium-high heat. Lightly oil grate. Grill chicken, turning once halfway through, until well charred and cooked through, 8–10 minutes. Transfer to a platter and let rest 5 minutes. If you have 6 chicken thighs, cut 2 of them in half and use 1½ thighs per sandwich.

Step 4

Grill buns cut side down until lightly charred, about 30 seconds. Transfer to platter with chicken.

Step 5

While chicken rests, coarsely chop fennel fronds. Toss fronds, sliced fennel, basil, red pepper flakes (if using), and remaining 2 tsp. oil and 2 tsp. lemon juice in a medium bowl; season with salt and black pepper.

Step 6

Spread reserved mayonnaise dressing on cut sides of each bun. Arrange 1–2 lettuce leaves and sliced tomato on bottom halves. Top each with chicken, then arrange fennel salad over. Close sandwiches with top buns.