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Measure the temperature of the oil with a candy thermometer. Using tongs or a mesh sieve, lower the brownie bite into the hot oil. Place the brownie bites on a plate that has been covered with three paper towels. The paper towels will absorb the oil from the brownie bites so that they do not turn soggy. Tap the side of the sieve so that the confectioner's sugar sifts through and dusts the top of the brownie bites.
Place a pan of oil in a Dutch oven and heat the oil to 375F (190C). Whisk together the flour, milk, sugar, baking soda and salt in a large bowl and place the bowl next to the stovetop. Remove the chilled brownies from the refrigerator and slice them with a butter knife into bite-sized pieces, about 1" (2.5 centimeters) in both length and width. Roll a brownie bite in the flour mixture until it is thoroughly covered. Continue battering brownie bites until the Dutch oven is full but not crowded. Fry the brownie bites for 3 to 4 minutes or until they are golden brown. Remove the brownie bites from the pan with tongs or a mesh sieve. Batter and fry additional brownie bites until you have completed the entire batch. Place confectioner's sugar in a sieve over the top of the brownie bites. Serve the bites warm on a small plate with a dollop of whipped cream, if desired.