Combine applesauce, sugar, cinnamon, lemon juice and butter in medium sized pot. Cook over medium high heat until it cooks down and most of the moisture has evaporated. Set aside.
To make the dough:
In bowl of large stand mixer, whisk together yeast, ½ cup flour, warm milk and sugar until smooth. Allow to stand 15 minutes until foamy (like the top of a latte). The presence of foam is the indicator that your yeast is good.
Mix beaten egg with the melted butter and salt. Add to the yeast mixture and stir to combine. Add 3 cups flour.
Using a dough hook, mix on low speed to combine ingredients and then knead dough, 5-6 minutes. If after a minute or so you have ingredients sticking to the sides or the bottom of the bowl, use a spatula to loosen and continue the mixing and kneading. Dough should be slightly sticky and elastic but not actually stick to a spatula when poked.
Transfer dough to another work surface. Wipe out bowl and drizzle olive oil. Form dough into smooth ball. Place in oiled bowl, cover with plastic wrap, and leave in warm room to rise and double in size, about 1-2 hours.
When ready to assemble monkey bread, punch down dough. Transfer to a floured work surface and cut into 64 pieces (cut in half, then each piece in half, etc until you have 64). roll each piece into a ball.
To make the monkey bread:
Butter or oil spray a 12-cup bundt pan. Combine the brown sugar and cinnamon from the coating ingredients in a small bowl. To assemble, take each dough ball, dip it in the melted butter, roll in brown sugar cinnamon mixture, and place in bundt pan. Add half the dough to the pan, top with half of the cooked down applesauce, add remaining dough balls, and finish with remaining cooked down applesauce. If there is any remaining melted butter or brown sugar, throw it in as well!
Cover pan tightly with plastic wrap and allow to rise at room temperature for at least an hour or in refrigerator overnight.
To bake, preheat oven to 350 degrees F, remove plastic wrap, and bake in preheated oven about 35-40 minutes or until top is deep golden brown.
Remove from oven, allow to cool in pan on wire rack for about 5 minutes, then invert onto plate.
To make the glaze, whisk ingredients together in small bowl. Drizzle over hot monkey bread on plate. Best if served warm and fresh!
Recipe for honeycrisp applesauce: https://selfproclaimedfoodie.com/honeycrisp-applesauce/