Add the butter, sugar, and water to a pot and bring everything to a boil. Add the flour and stir everything with a wooden spoon until the dough is smooth and comes off the wall of the pot. Once the dough has cooled, add the vanilla extract and one egg at a time. Mix everything once again with a spoon and transfer the choux pastry to a piping bag with a star-shaped tip.
Line a sheet pan with parchment paper, pipe 6 small cup handles on the parchment paper, and pop the sheet pan in the freezer. Grease the bottom of a muffin pan with a generous amount of vegetable oil and pipe the choux pastry around the individual molds. Make sure there are no gaps as you're piping, and you'll have to slightly press the end part to recreate the bottom of a cup.
Press the frozen cup handles into the sides of the choux pastry cups and freeze everything for at least 1 hour. Once the cups are frozen solid, remove them from the muffin pan molds.
Heat vegetable oil in a pot to about 325°F and fry the frozen churro cups in the hot oil, one at a time. Make sure that the whole cup is submerged in the oil – use a slotted spoon for extra help. Once the cup is golden brown and crispy, carefully remove it from the hot oil and immediately coat it in cinnamon sugar.
Heat the milk to about 150°F and pour it over the chocolate. Add the cinnamon and cayenne pepper and mix everything until combined. Fill the fried churro cups with the homemade chocolate sauce and top with a couple of mini marshmallows.