In a large bowl, sprinkle yeast over warm water. Mix in honey, oil, 2 eggs, and salt. Add flour one cup at a time, beating after each addition, graduating to kneading with hands as dough thickens. Knead until smooth and elastic, adding flour as needed. Cover with a damp clean cloth and let sit for 1 1/2 hours to rise.
Work down the risen dough and flatten out onto floured board. Divide dough in half and knead each half for five minutes, adding flour as needed to reduce tackiness. Divide each half into thirds and roll into long pieces (approx. 1 1/2 inches thick). Pinch the ends of the three pieces together firmly and braid from middle.
Place finished braids on 2 separate greased pans. Cover with towel and let rise about one hour.
Preheat oven to 375 degrees F. Beat the last egg and brush over each braid. Garnish with poppy seeds.
Bake for 40 minutes and cool on rack for at least one hour before serving.