In a bowl, combine the olive oil, vinegar, mustard, salt, pepper, & thyme. Whisk until smooth. Pour into a resealable bag.
Using a sharp knife, slice chicken breasts in half horizantally creating 4 thin cutlets. Place in the bag along with the marinade. Marinate in the refrigerator for 30 minutes while preparing the other ingredients.
In a small bowl, combine mayonnaise & pesto. Set aside.
Heat a pan on the stove on medium heat until really hot. Place the chicken (discard the marinade) in the pan & cook for a couple of minutes on each side until done & nicely browned. Place the cheese slices on top & let melt.
Spread the pesto mayonnaise on each side of the bread. Place lettuce leaves on the bottom halves of the rolls. Place the chicken on top of the lettuce. Top with 2 slices of bacon & sliced tomatoes.