Activate the yeast. Combine 1⅓ cups water, 2 Tbsp butter, ¾ cup sugar, and 1 package yeast in a large bowl, then whisk to combine. Let sit for 5 minutes.
Make the monkey bread dough. Meanwhile, place 3¼ cup flour and 2½ tsp Kosher salt in the bowl of a stand mixer fitted with hook attachment. With mixer on low, slowly drizzle in yeast mixture. When most of the flour is incorporated, increase speed to medium-high. Scrape down the sides, the mix for about 6 minutes, or until dough is extremely smooth and shiny. Use nonstick butter spray to coat the inside of a large mixing bowl. Transfer dough to prepared bowl, then cover with plastic wrap and let sit for 1 hour.
While dough is rising, make chocolate chip topping. Combine 1¼ cup brown sugar, 2½ tsp cinnamon, and 1¼ cup chocolate chips in a small bowl. Melt remaining stick of butter in a separate bowl.
Cut the dough. Roll out dough on a lightly floured surface into a 9x13 rectangle. Use a pastry cutter or bench scraper to cut dough into 1” squares.
Assemble the muffins. Gently roll each square into a ball, then dip in the remaining ½ cup melted butter. Immediately coat dough in the chocolate chip topping, then place in lined muffin cups, pressing down a little to make room for them all and filling to the top. Let dough rest for a half hour before baking.
Bake the monkey bread muffins. When ready, bake at 350°F/175°C for 18-20 minutes. Let cool in tray for 5 min, then carefully transfer to a wire rack.
Make the vanilla glaze. To make glaze, combine ¾ cup confectioner’s sugar, 2 Tbsp milk, and 1 tsp vanilla extract, then whisk until smooth. Add additional milk, 1 tsp at a time if you like a thinner glaze. Drizzle on top of warm monkey bread. Enjoy warm or room temperature.