Preheat oven to 400 degrees F. Sprinkle chicken with a bit of olive oil, season with salt and pepper.
Combine 2 TBS olive oil with mustard, reserving 2 tsp mustard for glaze. In a separate dish, combine remaining 2 TBS olive oil with bread crumbs and thyme, season bread mixture with salt and pepper.
In a large skillet, heat 1 TBS olive oil over medium-high heat. Sear the chicken, until crispy for about 2 1/2 minutes each side. Remove from heat, place in shallow baking dish. Smear each breast with mustard mixture, spread a thin layer of bread crumbs onto chicken. Turn chicken over, repeat both steps.
Place baking dish in the oven, roast until chicken is cooked through and the top is golden brown, 15-20 minutes.
While chicken is baking, mix together remaining 2 tsp Dijon and the sour cream. Stir until well-combined. Simmer over low heat for about 5 minutes until warm.
Place sour cream mixture on center of plate or platter in a very thin layer. Transfer the chicken to plates or serving platter on top of cream.