Preheat a large nonstick skillet or grillpan over med-high heat.
On a cutting board, combine 2 tablespoons chopped parsley, chopped chives, and chopped thyme; dip the tabs of cold butter into the herbs one at a time, pressing the herbs into the butter to coat them completely.
In a bowl, combine the ground chicken, Worcestershire sauce, 2 tablespoons mustard, salt, and pepper.
Form mixture into 4 large patties, no more than 1-inch thick.
Nest 1 herb-coated cold butter tab into the center of each patty and gently form the patty around the butter.
Drizzle olive oil over the patties and place them in a hot skillet/grillpan.
Cook 5-6 minutes on each side.
While burgers are cooking, combine the sour cream, lemon juice, dill, horseradish, and remaining mustard in a bowl; add in the radishes, red onion, carrots, cucumber, celery, coleslaw mix, and remaining 2 tablespoons chopped parsley, and salt/pepper to taste.
Toss to combine; serve the Kiev burgers open-faced on a slice of toast with the salad alongside.