Place a chicken breast half between 2 sheets of waxed paper; using the flat side of a kitchen mallet, pound the chicken firmly until it is about doubled in surface area and about 1/4 inch thick.
Remove chicken from waxed paper and trasfer to a clean work surface. Repeat with remaining chicken breasts.
Place 1 stick of herb butter along the short side of a chicken breast half. Starting at the short end, tightly roll the chicken up and over the butter. Continue to roll the chicken, folding the ends in a completely enclosing the butter.
In a shallow dish, combine almond flour, salt and pepper. In another shallow dish, beat egg with water.
Dip chicken rolls in egg wash to coat; dredge in seasoned flour mixture, patting so crumbs adhere. Cover chicken; chill at least 1 hour.
Pour oil into a skillet. Heat over medium-high heat. Add chicken in batches, being carful not to overcroud; fry in skillet until chicken is cooked through. Serve immediately.