Prepare you fry station in this order: flour seasoned with salt & pepper, eggs beaten and seasoned with salt & pepper, panko combined with parm and seasoned with salt and pepper.
Add oil to a fry pan, and heat to 300°F. Once oil has reached temp; season a chicken breast, dredge in flour, then eggs, then panko parm and place in fry pan. Cook for until golden brown, flip breast.
Continue cooking until chicken reaches 155°F (about 8-10 minutes)- it will reach 165°F at rest. Set breast aside on cooling rack or paper towels; season with salt and pepper.
Repeat process with remaining chicken breasts.
Chicken Parm Sandwich Plating
Pre-heat oven to 400°F.
Cut the very end off of each tomato. Place a box grater on to a plate; place the cut side of the tomato against the largest holes and grate directly onto the plate. Discard the peel, and season the tomato pulp with salt and pepper.
In a cast iron pan, melt butter, and toast all brioche buns.
Place burrata on a plate; divide burrata cheese into four sections while remaining on the plate (curd with start to spill out).
Cover a small cookie sheet with foil. Place all fried chicken breasts on foil. Spoon 1/4 of the burrata (curds and all) on to each chicken breast. Place sheet in oven. Once burrata has just started to bubble and melt, pull chicken out.
For each sandwich: Place 5-6 whole basil leaves on bottom brioche bun. Place chicken breast with burrata directly on top. Spoon the grated tomato on top of the chicken. Finish with the top brioche bun.