Brine chicken breasts by filling a large bowl with 1 quart of warm water and 1/4 cup of kosher salt. Stir until salt is absorbed. Add chicken breasts and let them brine for 20 minutes. Remove breasts from the brine, rinse, and pat dry with paper towels.
Pre-heat oven to 450 degrees F.
Coat baking dish with olive oil. Place breasts in a single layer in large baking dish. Brush both sides with extra virgin olive oil.
Season each breast on both sides with kosher salt, course ground black pepper, and smoked paprika.
Whisk together 1/3 cup of red wine jelly with 2 ½ TBPS of hot mustard.
Coat the top side of each breast with one half of the jelly mustard mixture. Bake for 10 minutes in the lower third of the oven.
Remove baking dish from the oven and turn the breasts over. Coat this side of each breast with the remaining jelly mustard mixture and return dish to the oven.
Bake for 8-10 minutes longer. The thickest part of the breast should register between 160-170 degrees F when measured with an instant read cooking thermometer.
Remove pan from the oven and loosely cover with foil. Let the chicken breasts stand for 10 minutes.
Slice the breasts into medallions and serve immediately.