Preheat oven to 375° F. Line a 9x5-inch metal loaf pan with parchment paper or spray with flour-based cooking spray.
In a measuring cup, whisk together the milk and lemon juice. Set aside. The milk will thicken and curdle slightly as it stands; this is normal.
In a medium mixing bowl, combine the dry ingredients - whole wheat flour, rolled oats, dark brown sugar, baking soda, baking powder, and salt.
In a large mixing bowl, gently stir together the milk/lemon juice mixture, melted butter, vanilla extract, and Irish stout beer.
In the large mixing bowl, add the dry ingredients to the wet ingredients. Stir until fully incorporated; the bread batter will be thin, like cake batter. Pour batter into the prepared loaf pan.
Bake in the preheated oven for 35 minutes.
When the 35-minute baking time is done, without removing the bread from the oven, reduce the temperature to 325°F. Continue baking for an additional 35 minutes.
When the second 35-minute round of baking is done, leave the bread in the oven, turn off the heat, and open the oven door. Let the bread to cool down slowly in the oven for 30 minutes.
Remove bread from the oven, then carefully turn it out onto a wire rack. Serve warm or at room temperature.