In a large bowl, sprinkle the yeast over warm water and let stand 5-10 minutes, until it bubbles. Using a wooden spoon, stir in melted butter, sour cream, sugar, egg, and vanilla until well combined.
Stir in 2 cups of flour with wooden spoon until combined. Add remaining ½ cup flour and mix until dough is uniform, about 3-4 minutes.
Place the dough onto a lightly floured surface and knead until smooth, about 3 minutes. If the dough is sticky, add flour ½-1 teaspoon at a time. (I did not need extra flour other than my floured surface.)
Once dough is smooth, place in the mixing bowl and cover bowl with plastic wrap. Let dough rise in a warm place until doubled in size, about 1 hour.
With butter, lightly grease a 12-cup muffin tin then add flour, tapping out excess flour.
In a medium sized bowl, mix together the sugar, cinnamon, and vanilla. Vanilla may seem to make it wet, but it will return to a crumbly texture.
Melt butter in a small dish and set aside.
Make the Monkey Bread Muffins:
Gently punch down dough, about 4-5 times. Divide dough into 12 equal pieces. Using a sharp knife, divide each of the 12 pieces into 6 equal pieces. Roll each piece into a ball.
Each muffin will use six balls. Roll each ball in melted butter to coat generously, and drop into the cinnamon mix, tossing to coat.**
Place five balls in the bottom of the muffin tin around the outside, and nestle a sixth ball in the middle of the 5 balls snugly, pushing it in carefully so that it is even with the outer 5 balls.
Once all muffins are prepared in the muffin tin, sprinkle remaining sugar mixture over top of the muffins. Using plastic wrap, loosely cover muffins and let muffins rise in a warm place until doubled in size, about 40 minutes. Meanwhile, preheat oven to 350°F.
Place the muffins on the center rack of the oven, and turn the oven down to 325°F. Bake until golden, about 20-22 minutes.
Transfer the muffin tin to a wire cooling rack to cool for 5-10 minutes. Carefully turn the monkey bread muffins out onto a cookie sheet (or parchment or wax paper). For any that don’t come out, carefully run a knife around the edges until they’re ready to come out. With the sugar, you may find they need a bit of help. Place on the wire cooling rack.
In a small bowl, mix the glaze ingredients until smooth. If you prefer a thinner glaze, use 1 teaspoon of milk to thin it out. Drizzle glaze on muffins.
Serve immediately or at room temperature.
*May substitute brown sugar for white sugar**Use plenty of butter and squish the dough balls together before allowing to rise for best results