Add the sugar to the warm water and then stir in the yeast. Allow to sit for 5–10 minutes or until it foams. Combine oil and honey. Mix with yeast and then pour into mixer bowl with flour and salt. Combine in mixer on low speed with the dough hook for 2 minutes.Stir together 2 of the whole eggs and all 3 yolks. Add half of the egg mixture to mixer and continue to mix. After eggs are fully incorporated, add second half of egg mixture and mix for 6 minutes. Remove dough from bowl and knead for a few minutes on a floured surface. Place dough in a greased bowl and cover with plastic wrap.Let dough rise in a warm place until doubled in size. Divide the dough into 2 pieces for the 2 loaves, and then for a four-piece braid, divide each dough loaf into 4 pieces. Roll the pieces into approximately 12-inch rolls tapered at the ends and thickest in the center. Lightly dust each piece with flour to keep from sticking. Line the four pieces next to each other and, beginning in the middle, number the strands 1-4 from left to right. The number for each strand will change as the strand moves in the next step.To braid, follow this pattern: strand 4 over strand 3, strand 2 over strand 3, strand 1 under strands. Repeat to the end then tuck the ends under. Rotate the loaf and repeat on the other side. Lightly dust tops of loaves with flour and cover loosely with plastic wrap. Place in the refrigerator overnight or let rise in a warm place.Combine the remaining egg with 1 tablespoon milk and gently brush on the loaves. Top with poppy or sesame seeds and bake at 350 degrees for 30-40 minutes or until golden brown. Halfway through, brush with wash again for an even deeper golden bread.