In a shallow bowl stir together All-Purpose Flour (1/3 cup), Salt (1/2 teaspoon), and Ground Black Pepper (1/4 teaspoon). Set aside.
Cut off fillet from Chicken Breast (1 pound) if attached. Slice each chicken breast horizontally into two pieces.
Cut each piece in half, giving 4 pieces of similar size per chicken breast, plus the fillet if included.
Place each piece, including fillet between two pieces of parchment paper. Pound with a flat mallet until 1/4" thick.
Heat Canola Oil (1 tablespoon) a large skillet over medium high heat.
Toss chicken pieces in the flour mixture and shake off excess. Fry half of the chicken pieces 2 minutes per side and remove to plate and keep warm. Repeat with remaining Canola Oil (1 tablespoon) and chicken.
Reduce heat to medium and add Unsalted Butter (1 tablespoon) to pan, add Shallot (1) and sauté for 1 minute until softening but not browning.
Add White Wine (1/2 cup), stirring and scraping the pan to remove all the cooked bits. Stir in Chicken Broth (1/2 cup) and reduce for 3-4 minutes until it reduces to about half the size.
Whisk in Dijon Mustard (2 teaspoon). Then whisk in the remaining Unsalted Butter (3 tablespoon), 1 tablespoon at a time, allowing each to incorporate before adding more.
Stir in Lemon Juice (1 tablespoon) and chopped Tarragon (1/4 cup). Season with salt and pepper. Add chicken cutlets back to pan and spoon with sauce.