Stir together 1 Tablespoon canola oil and 1 Tablespoon all-purpose flour in a small bowl to form a runny paste. Brush the mixture all over the inside of a 12-cup bundt pan. Set aside.
Brazilian Carrot Cake
Move an oven rack to the middle position and turn the oven on to 350°F.
Add 2½ cups shredded carrot, 1½ cups granulated sugar, ½ cup canola oil, ½ cup plain or vanilla Greek yogurt, and 3 large eggs to a blender or food processor. Puree until the mixture is smooth and no large chunks or shreds of carrots remain.
In a large bowl, whisk together 2 cups all-purpose flour, 1 Tablespoon baking powder, ½ teaspoon salt, and ½ teaspoon baking soda. Whisk the carrot mixture into the flour mixture until smooth. Before pouring the batter into the prepared bundt pan, brush the pan release mixture up the sides one more time, making sure that there are no pools of the mixture at the bottom of the pan. Pour the batter into the pan and smooth the top of the batter with a spatula, if needed.
Bake the cake on the middle rack of the oven for 45-50 minutes, until a toothpick inserted into the center of the cake comes out with crumbs clinging to it. Cool the cake in the pan for 15 minutes, then turn the cake onto a wire rack set over a foil-lined baking sheet and cool to room temperature, about 30 minutes.
Chocolate Brigadeiro Frosting
While the cake is cooling, start making the frosting. Pour 1 can sweetened condensed milk, ½ cup whole or 2% milk, ½ cup granulated sugar, ½ cup cocoa powder, 4 Tablespoons unsalted butter, and ¼ teaspoon salt into a medium saucepan set over medium heat. Cook the mixture, stirring constantly until it comes to a boil, about 10 minutes. Reduce the heat to medium-low and continue to simmer until the mixture is thickened, about 5-10 more minutes. Remove the saucepan from the heat and stir in 1 teaspoon vanilla.
While the frosting is still hot, pour it slowly over the cake. I found it best to do this in multiple layers, as the frosting will build up as it cools. Note that you can scrape any frosting that flows off the cake from the foil back into the bowl to re-pour onto the cake, or save for another use (it's great over ice cream). As soon as you're done adding frosting, make sure to add the chocolate sprinkles before the frosting sets. Let the cake sit for 30 more minutes before serving for the frosting to set.