Mix together the flour, quick-rise yeast, sugar, and salt in a mixing bowl. Put the oil together with the warm milk (110℉) in a glass measuring cup. Slowly add all the oil and milk into the flour mixture while mixing to form a loose dough. Turn onto a lightly floured counter and knead until a smooth dough forms - about 1 minute of kneading.
Shape dough into a ball and place in a bowl that has been well greased with oil (seam side down). Cover with plastic wrap and let rise in a warm place for 1 hour.
When the dough is done rising, preheat the oven to 375℉. Grease a 12-count muffin tin with non-stick spray or use cupcake liners.
Punch down the dough to deflate all air pockets. Place the melted butter in a small bowl and mix together the brown sugar and cinnamon in another small bowl.
Cut off small pieces of dough (each about the size of your thumb, for lack of a better size reference), dip each piece in the melted butter and then roll each in the cinnamon sugar to coat before placing in the muffin cup. Each cup of the muffin tin should have about 5 or 6 pieces or just distribute the pieces evenly between all cups. Repeat until all the dough is used up (you may need to use a bit more brown sugar and cinnamon if you run out).
Bake the muffins immediately in the preheated oven for 15-17 minutes or until bubbly and fully cooked on the inside. Let cool in the pan for at least 10 minutes before topping with the icing (instructions below), if desired. Enjoy!
To make the Icing:
Stir together the powdered sugar and whipping cream until smooth. Drizzle over the slightly cooled muffins using a spoon or a ziplock bag with the corner snipped.
Notes
These Monkey Bread Muffins are best served warm out of the oven but will stay covered at room temperature for up to 3 days. I recommend warming them up again before serving if you are saving some for later.