In the bowl of a stand mixer, whisk together butter, milk, yeast, sugar, salt, egg, and yolk until blended. Add flour and use a dough hook to bring the mixture together and knead on low speed for 5 to 7 minutes, until dough is stretchy but soft. Transfer to an oiled bowl, cover tightly with plastic, and set aside for 1 1/2 to 2 hours in a warm spot, until just about doubled. While the dough rises, cook your onions. Melt butter in a large sauté pan over medium heat. Add the onions, toss to coat them in butter, and cover the pot. Reduce the heat to medium-low and let them slowly steep for 12 to 15 minutes, stirring once or twice. Uncover the pot, raise the heat slightly and stir in salt. Cook onions, stirring every 5 minutes for another 20 to 30 minutes, until golden brown and very tender and sweet. Raise the heat to medium-high and cook the onions until they get a little dark at the edges, about another 5 minutes. Transfer onions to a plate and spread them out so that they cool faster. On a large, well-floured counter, roll out the dough until it is about 12 inches wide and as long in length as you can when rolling it thin, likely 10 to 14 inches. Spoon then spread onions over the dough in an even layer, then sprinkle onions with 2 teaspoons poppy seeds. Roll the dough up with the filling away from you into a tight coil. Transfer the coil to a parchment-lined baking sheet or board to your freezer, just for 5 to 10 minutes. Prepare the pan by coating a standard loaf pan with butter or nonstick spray, and line the bottom and two sides with a sling of parchment paper for easier removal. Remove dough from freezer and use a serrated knife to gently cut the log lengthwise into two long strips and lay them next to each other, cut sides up. Lift one side over the next, forming a twist and trying to keep the cut sides facing up. Transfer the twist into your prepared loaf pan. Cover the pan with plastic wrap and let it rise another 45 minutes at room temperature. Heat your oven to 350°F. Sprinkle babka with an extra couple pinches of poppy seeds. Bake for 40 to 45 minutes, until a skewer inserted into the center doesn’t feel like it’s hitting sticky/rubbery dough, or the internal temperature is 185°F. Let cool and then cut into thick slices with a serrated knife. Wrap leftovers in foil.