Preheat oven to 275F.

Place your chicken breasts in a baking dish large enough to hold them in one layer.  Pierce each one in the thick end 4-6 times with a fork, all the way through.  Sprinkle 1/2 tsp onto each chicken breast (total for both sides).  Cover with foil and place in oven for 30-45 minutes.  

When the chicken internal chicken is 145F-150F, remove from baking dish to a paper-towel-lined plate; pat dry.

Heat a skillet large enough to hold all four chicken breasts in a single layer (12" or so) with 1T of vegetable oil over medium-high heat until it was just smoking.

Mix together melted butter, 1 T flour, cornstarch, and pepper.  Brush onto one side of all four breasts.  Place chicken breasts, buttered side down, into hot skillet.  Leave alone for 3-4 minutes, until the underside is a nice golden brown.  Brush remaining butter mixture onto exposed sides of chicken in pan, then flip, lower the heat to medium and leave alone for 3-4 minutes until both sides are nicely golden brown.  Keep cooking until they are 165F in the middle.

Remove chicken breasts to a plate, let them rest.

Add shallot, let it soften about 2 minutes.  Add 1t flour, mix until smooth.  Add chicken broth slowly (to avoid lumps of flour).  Simmer about 3-5 minutes until it thickens and reduces to about 3/4 cup.  Add all the juices from the plate the chicken has been resting on.  Finish sauce with lemon juice, chives, 1 T butter.

Serve with a bit of sauce drizzled over each chicken breast.