Preheat oven to 350 degrees and lightly spray or brush a doughnut pan with cooking oil.
In a large bowl, whisk together flour, sugar, baking powder, and salt.
In a separate medium bowl, mix together sweetened condensed milk, whole milk, egg, melted butter, vegetable oil, butter extract, and vanilla extract.
Stir the wet ingredients into the dry ingredients until just combined, taking care not to over-mix (over-mixing can result in tough donuts).
Divide donut batter into two equal portions and place in separate bowls. Add a few drops of yellow food coloring to one bowl of batter and gently mix in until evenly colored. Add orange food coloring to the other bowl and gently mix until evenly colored.
Add the orange batter into one side of a piping bag fitted with round tip (or in a Ziplock bag with the corner cut off) and the yellow batter to the other side.
Pipe the swirled donut batter into the prepared pan, filling each cavity about ¾ of the way full.
Bake donuts for 9-12 minutes, until they're lightly golden and light and springy to the touch. Let donuts cool in the pan for a few minutes and then remove to cool completely on wire rack. If you're using a 6-cavity donut pan, repeat with remaining batter.
Once doughnuts are completely cooled, dip upside-down in icing to coat. Set on wire rack with waxed or parchment paper set underneath and top donuts with sprinkles, if desired.