Place bite-sized pieces of chicken breasts in airtight container. Cover with pickle juice and seal container. Place in refrigerator and let chicken marinate in pickle juice at least 1 hour, up to 8 hours.
Add mayo, Dijon mustard, keto honey, apple cider vinegar, and cayenne to small bowl. Whisk until ingredients are well-combined, then cover bowl and refrigerate until ready to serve.
When chicken has marinated for desired length of time, remove container from refrigerator. Crack eggs directly into shallow bowl and whisk until egg wash is pale in color and eggs are no longer streaky. Set egg wash aside.
Add almond flour, parmesan cheese, salt, garlic powder, onion powder, and paprika to second shallow bowl. Whisk ingredients together until well blended. Set aside.
Drain pickle juice from container and discard. Working in batches, take handfuls of marinated chicken and place in egg wash. Be sure to separate pieces of chicken so egg wash can coat all sides.
Transfer chicken pieces from egg wash to breading mixture, allowing any excess egg wash to drip back into bowl before moving to next bowl. Coat pieces of chicken in flour mixture, covering all sides completely. Shake any excess flour mixture back into bowl and place breaded chicken pieces on plate. Repeat until all pieces of chicken have been breaded.
Heat large skillet over medium-high heat. When skillet is warm, add approximately ½-inch of oil to cover entire bottom of skillet. Continue warming pan until oil is hot and shimmery.
While pan and oil warm up, cover plate with 2 to 3 layers of paper towels. Place wire cooling rack over paper towels and set aside.
Once oil is hot, add breaded chicken nuggets to skillet, working in batches to avoid overcrowding. Pan-fry chicken nuggets approximately 3 to 4 minutes, then flip chicken over and pan-fry another 3 to 4 minutes or until breading is golden brown and chicken is cooked through.
When chicken is cooked through, transfer chicken to wire cooling rack. Repeat process until all chicken nuggets have been fried, adding more oil to skillet when necessary. Be sure to let oil reheat after each batch of chicken nuggets, or breading will come out soggy.
Once all chicken nuggets have been fried and excess oil has dripped off, divide chicken into desired portions. Serve warm with keto honey mustard sauce and any desired sides.