Preheat the oven to 450°F and line a large rimmed baking sheet with aluminum foil.
In a large bowl, whisk together 1/3 cup Dijon mustard, 1/3 cup mayonnaise and the pressed garlic cloves; set the marinade aside to let the garlic infuse.
Place the bread crumbs in a separate shallow bowl or dish for coating.
Rinse and pat the chicken breasts dry, trim any excess fat, then cut into 1-inch thick strips; lightly season both sides with sea salt and black pepper.
Toss the chicken strips in the mustard-mayo-garlic marinade until evenly coated.
Roll each strip in the bread crumbs, pressing so the crumbs adhere; repeat if needed for an even coating, then place the breaded strips on the prepared baking sheet without overcrowding.
Bake at 450°F for 15–17 minutes, or until the chicken is cooked through and golden brown on the outside.
Meanwhile, in a medium bowl (or blender) combine 1/3 cup Dijon mustard, 1/3 cup honey and 1/3 cup mayonnaise; stir in the poppy seeds if using, then refrigerate the dip until ready to serve.