Dough. Pour water into mixing bowl of electric mixer. Cover with yeast and about ½ tsp. of the sugar. Stir gently to hydrate the yeast. Let it sit for 5-10 minutes to get foamy. (If using instant yeast, skip this step and mix your yeast and water in with everything else in the next step.)
Add the yolks, oil, honey, sugar, and flour. With the dough hook attachment, knead the mixture for about 4-5 minutes.
With the mixer on low, slowly add the salt. Knead for an additional 2-3 minutes until the salt is fully absorbed and the dough passes the windowpane test.
Place dough in ungreased bowl, cover with plastic wrap, and let rise in warm area for about 3 hours.
Onion filling. Toss all ingredients in a medium frying pan. Remove 3 tbsp. of the mixture and store on counter in plastic wrap. (The raw onion mixture will be used to sprinkle on top of the rolls.) On a medium-low heat, cook remaining onion mixture until onions are translucent and just begin to caramelize on the sides, 5-7 minutes. (The cooked onion mixture will be used for filling the rolls.)
Line the bottom of a 9 inch by 13 inch baking pan with parchment paper.
Gently deflate the dough. Divide into 12 equal portions (approximately 60 g. each) and shape into balls. Cover with plastic wrap and allow to rest for 5 minutes.
One ball at a time (while keeping the others covered with plastic wrap), pat down the ball into a flat oval. Use about 1 tsp. of the onion mixture to fill each roll. Lay the onion mixture across the top third of the oval. Fold the top third of the oval over itself. Fold the left and right sides over itself and pinch the dough to make sure it is fully enclosed. Fold up the bottom and again pinch the edges to ensure it is fully enclosed. (Alternatively, you can flatten the dough into a circle/oval, place the onion mixture in the middle, and pull the edges into the middle, connecting them but not touching any of the onion mixture.) Use your hand to cup the ball against the countertop with your fingers and thumb closing in on the base of the ball. Rotate it clockwise to round out the ball. Repeat with remaining balls of dough, placing each ball in the prepared pan a couple of inches apart from each other and from the sides of the pan.
Cover loosely with plastic wrap and let rise 1 hour.
Preheat oven to 350° F.
Apply egg wash. Sprinkle each roll with uncooked onion mixture. Bake 28-32 minutes.