In medium bowl, whisk together 2 tablespoon lemon juice, Dijon mustard, Worcestershire sauce, garlic and black pepper. Slowly pour in 1/3 cup olive oil, whisking constantly until marinade is emulsified. Season with salt, to taste.
Transfer half of marinade to another bowl; place chicken thighs in marinade mixture, turning to coat all over. Let stand at room temperature for 30 minutes (or cover and refrigerate marinated thighs for up to 4 hours).
To remaining lemon garlic mixture, whisk in mayonnaise and cornichons. Set aside.
Preheat Vida by PADERNO Wi-fi Connected Smart Pellet Grill over medium-high heat.
Remove chicken from marinade, discarding excess marinade. Place thighs on greased grill; close lid.
Cook chicken thighs 4 minutes. Turn them over; grill an additional 4 minutes, or until deeply browned.
Reduce heat to low; continue cooking until an instant read thermometer inserted in thickest part of thigh registers 180°F, about 5 minutes longer.
Transfer thighs to a platter; keep warm.
Place brioche buns on grill, cut side down, until lightly toasted, about 30 seconds.
In bowl, toss together fennel and fronds, basil, the 2 teaspoons remaining olive oil, and 2 teaspoons remaining lemon juice to combine. Season with salt and pepper, to taste.
To assemble, spread cornichon dressing on cut sides of toasted buns. Sandwich with chicken and fennel salad.
