To make the dough, add water to the bowl of a standing electric mixer. Scatter yeast and a pinch of the sugar over the water’s surface. Stir to combine. Let stand until bubbly, about 5 minutes.
Meanwhile, melt butter in a small saucepan over medium heat. Remove from heat and add milk, sugar, and salt. Stir to combine. Add egg and mix well.
Add contents of the saucepan to the yeast mixture along with 2 cups of the flour. Beat with the paddle attachment until combined. Add remaining flour, about a half a cup at a time, until a smooth but sticky dough forms. Switch to the dough hook and knead for 3 to 5 minutes. Transfer the dough into a greased bowl, flipping it to coat the entire surface with oil. Cover with plastic wrap and let rise until doubled in size, about 1 to 2 hours.
To prepare for assembly, combine sugar and spices in a wide, shallow bowl. In a separate bowl, melt the butter. Lightly brush the inside of a large tube or bundt-style pan with a bit of the melted butter. Turn out the dough onto an unfloured surface and gently deflate it. Shape the dough into scant one-inch balls (I ended up with 84).
Dip the balls, one by one, in the melted butter and then roll them in the brown sugar mixture. You may need more of the sugar mixture depending how generously you coat each ball. Drizzle any remaining butter over the top of the filled bundt pan.
Bake right away in an oven preheated to 375° F until golden brown on top, about 35 to 40 minutes. Let rest for 5 to 10 minutes in the pan before inverting it onto a platter. Let the bread cool briefly before serving as the sugary syrup will be extremely hot.