In a large bowl, combine the eggs, oil vanilla extract, and both sugars. Mix in a stand mixer, or hand mixer on medium for 2 minutes.
4 large eggs, 1 cup vegetable oil, 1 cup brown sugar, 2 teaspoon vanilla extract, 1 cup granulated sugar
Add ⅓ of the dry ingredients mixture to the eggs mixture, and mix on medium to combine. Add about half of the milk and mix on medium to combine. Add another third of the dry ingredients, and mix to combine. Add the remaining milk, and mix to combine. Add remaining dry ingredients, and mix to combine.
¾ cup whole milk
Pour the batter into the prepared pans, Only fill the mini bundt cups up to ⅔ full.
Bake for about 35-40 minutes for the large pan, 20-30 minutes for mini pans. Remove when the cake begins to pull away from the pan along the edge. While holding the pan in both hands rotate in a circular motion a few times.
Move pan to a cooling rack for about 10 mins, then remove the cake from the pan and let it cool completely on the rack.
brown sugar frosting
In a medium saucepan combine butter, brown sugar, and milk. Heat over medium heat, stirring constantly until brown sugar is melted completely. Remove from heat immediately and allow to cool completely.
1 cup butter, 1 ½ cups light brown sugar, ⅓ cup whole milk
Pour the cooled mixture into a large mixing bowl, add vanilla and about half of the powdered sugar. Mix at low speed until combined, adding more powdered sugar as needed to reach desired consistency.
1 teaspoon vanilla, 4 cups powdered sugar
Drizzle frosting over the top of the cake(s) allowing it to drip down the sides.
Notes
Makes one 10 cup bundt cake or 12 mini sized ones.