• Combine one tablespoon of sugar (from the ¼ cup), yeast, and warm milk in the bowl of a stand mixer for 5 minutes to activate the yeast. Once foamy, add the remaining sugar, egg and yolk, flour (2¼ cups), and salt
• Using the dough hook attachment, mix on medium speed until it comes together into a rough ball. 
• Turn the speed one click lower, then add 1 tablespoon of the softened butter at a time. Wait to add the next piece of butter until the prior piece is mostly incorporated. 
• Mix on medium high speed until the dough is smooth, scraping down the sides and bottoms a few times. If the dough hasn't come together, increase the speed and keep mixing.
• When it’s ready, the dough should completely be pulled away from the sides and mostly or fully off of the bottom. If a bit is still sticking to the bottom of the bowl, that's ok. However, if it's very sticky, add an additional tablespoon of flour at a time until it mostly removes itself. The dough will be soft and supple when it’s ready.
• Form the dough into a ball and place in an oiled bowl, cover with plastic wrap, and rest in a warm location for about 30 minutes.
• Right before rolling out the dough, make the pistachio filling.

Pistachio Filling

• Add the pistachio butter, powdered sugar, melted butter, almond extract, and a touch of green food coloring to a bowl and mix well to combine. Add more food coloring, until the desired color is reached.
• Prepare a standard loaf pan with a strip of parchment paper overhangs and set aside.

Assembly

• Lightly flour your work surface and rolling pin, shape the dough into a rectangle with your hands, then roll the dough out into a 10x14 inch rectangle. Use a bench scraper to keep the dough in a rectangle shape.
• Once rolled out, spread the filling evenly over the dough with an offset spatula, taking it to the edges.
• Starting from one of the long edges, tightly and evenly roll the dough into a log. Pinch the seam together to seal, then turn and place the seam side on the counter. Gently push the dough inwards from each side, just to re-compact the log a bit.
• Cut the entire log in half lengthwise and place each piece in line with each other so the filling side is up. Pinch the top edges together, then, keeping the cut sides up, twist each piece of dough around each other as many times as possible. Pinch together the bottom pieces to seal.
• Place the dough in the prepared loaf pan. If it's too long to fit in, just tuck one of the edges next to it like an “s”.
• Cover the dough with plastic wrap and allow it to rise in a slightly warm location for about 1 hour until the dough puffs up and starts to fill out the pan a bit. If your kitchen is rather cold, try another room in the house, or allow it to rise in a closed oven (no heat) with just the light on.
• Preheat the oven to 375°F/190℃, uncover the loaf, and bake for 25-30 minutes in the middle rack. The babka is done when you can insert a sharp knife and it has little resistance. If it still feels at all stretchy or doughy when you poke it in, allow it to bake for another 3-5 minutes and check again.

Simple Syrup

• As soon as the babka goes into the oven, make the simple syrup. Add the water and sugar in a small saucepan and heat and stir until the sugar dissolves, then cool completely. Stir in the almond extract once cool.
• As soon as the babka comes out of the oven, brush or spoon the simple syrup over the top, getting every nook, cranny, and edge, until it’s gone. It may feel like too much syrup, but it’s not! Cool in the pan, then slice and enjoy.