To make beurre blanc, add finely chopped shallots to medium saucepan with 1/2 tablespoon unsalted butter, then lightly salt and pepper and heat on medium-low.
Once shallots are slightly soft, add finely minced garlic and once aroma releases (1 minute or so), add wine and white-wine vinegar. Raise heat to medium and allow to simmer.
Once liquids are reduced by half, add cream, lemon juice, salt, and white pepper; and again reduce by half.
Remove saucepan from heat and whisk in unsalted butter 1 tablespoon at a time until melted. Continue until 2 sticks are added and melted. Set saucepan aside, off heat.
Tenderize pheasant breasts with meat mallet and flatten to 1/4 inch depth.
Beat two eggs in a bowl. Place flour (with salt and pepper) in another bowl. Place Panko bread crumbs in a third bowl (three-stage process prior to frying).
In a deep skillet, add a thin layer (approximately 1/4 inch) of clarified butter OR cooking oil with a couple tablespoons of butter. Heat on medium to 375-400 degrees Fahrenheit.
For each pheasant breast, dip each side in egg wash then in flour. Shake off excess flour, then coat in Panko and add to skillet (do NOT add before butter or oil/butter reaches near 400). Fry to golden crisp then flip, repeating on other side. Place on napkin-covered plate until ready to serve.
Right before serving, pour sauce through a sieve into a medium bowl. Press shallots and minced garlic against sieve and discard after all sauce has been through sieve. Add back to saucepan.
Add capers to beurre blanc. To serve, add fried pheasant breasts to plate and top with beurre blanc (now containing capers).