Slice feta into four fingers and place in the freezer for 10 minutes to help the cheese hold its shape while you prepare the other ingredients.
Set out egg, flour, and sesame seeds in three separate shallow dishes. Season egg with black pepper.
Pour oil into a small skillet to a depth of about 1/2-inch. Heat over medium-high heat.
Remove feta from freezer and dredge each finger first in egg, then flour, egg again, followed by sesame seeds. Evenly coat all sides. Add breaded fingers to the hot oil.
Cook until golden brown, about 2 minutes per side. Remove from oil and briefly drain excess oil on kitchen towel.
Place feta fingers on a serving plate and drizzle with honey. Enjoy immediately while hot.