For the Starter:
Mix yeast, sugar, and warm water in a small mixing bowl. Set aside for 10 minutes to allow yeast to proof. Bubbles will form at the surface.
For the Dough:
Mix the bread flour and salt in large mixing bowl. Put the mixture in the bowl of a standing mixer fitted with the hook attachment. With the mixer set on medium speed, slowly add the Starter to the dry ingredients, followed by the milk, egg, and melted butter. Add the dill and mix on medium speed just until the dough releases from the side of the bowl, about 5 minutes. Transfer the dough to a lightly greased bowl, cover the bowl with plastic wrap, and put in a warm place. Allow dough to rise for 30 minutes.
For the Monkey Bread Loaves:
Preheat the oven to 375ºF. After the Dough has risen for 30 minutes, punch it down and roll into 32 balls, about 1 inch in diameter. Mix half the melted butter and all the dill together. Roll the dough balls in the mixture and arrange in 8 lightly greased 4-ounce aluminum loaf pans (9 balls per pan). Allow the loaves to rise once more in a warm spot for 20 minutes. Sprinkle the loaves with sea salt and bake for 12 minutes, brushing twice throughout the baking process with the remaining melted butter.
To Assemble and Serve:
Serve loaves hot out of the oven with more melted butter and fresh dill.