Attach the dough hook attachment to your stand mixer.
In the mixing bowl of the stand mixer, combine 3 cups of flour, sugar, salt, and yeast.
In a separate bowl, whisk together the warm milk, melted butter, eggs, and vanilla extract.
With the stand mixer on low speed, gradually pour the wet ingredients into the dry ingredients. Mix until a dough forms.
Increase the speed to medium-low and knead the dough for about 5 minutes, or until it's smooth and elastic. If the dough is too sticky, gradually add the remaining ½ cup of flour until it reaches the desired consistency.
Place the dough in a greased bowl, cover it with a clean kitchen towel or plastic wrap, and let it rise in a warm place for about 1 hour, or until doubled in size.
Follow steps 7 through 12 of the original recipe, shaping the dough into balls, dipping them in butter, and coating them in the cinnamon-sugar mixture.
Arrange the coated dough balls in a greased Bundt pan, cover it, and let it rise for another 30-45 minutes, or until puffy and almost doubled in size.
Preheat your oven to 350°F (175°C). Bake the monkey bread in the preheated oven for 30-35 minutes, or until golden brown and cooked through.
While the monkey bread is baking, prepare the glaze by whisking together the powdered sugar, milk or cream, and vanilla extract until smooth.
Once the monkey bread is done baking, remove it from the oven and let it cool in the pan for 5-10 minutes. Invert the monkey bread onto a serving platter and drizzle the glaze over the top.
Serve the monkey bread warm, pulling apart the pieces to enjoy the gooey goodness!
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