Preheat oven to 350F and grease a 9x4-inch loaf pan. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment (or in a large mixing bowl with an electric hand mixer), mix together oil and sugar until combined.
Add eggs, vanilla extract, and almond extract. Mix to combine.
In a separate mixing bowl, whisk together flour, baking powder, salt, and dry pudding mix.
With the mixer on low speed, gradually add half of the dry ingredients to the wet ingredients. Mix in 5 tablespoons of milk, then mix in the remaining half of the dry ingredients just until combined.
Measure out one cup of the batter and transfer it to another small mixing bowl. Set aside.
In a liquid measuring cup, whisk together 4 tablespoons of milk and the cocoa powder until combined. Add this mixture to the one cup of batter, stirring to incorporate.
Add one tablespoon of milk to the remaining green batter in the main mixing bowl, stirring to incorporate.
Layer the two batters in the loaf pan (I use a spoon to drop dollops of both colors of batter into the pan), then use a knife to gently swirl the batter (I make an "S" shape with the knife). Don't swirl too much or the batters will bleed together.
Bake in preheated oven for 55-65 minutes, or until a toothpick inserted in the center comes out clean.
Let cool in the pan for about 10-15 minutes, then run a knife along the edge of the loaf to ensure it's loosened from the pan. Remove loaf from the pan and cool completely before slicing.