Prepare the Korean Banana Milk: Peel the banana and place it into a blender. Add maple syrup, vanilla extract, cold milk, and cold water. Blend until smooth and creamy.

Taste the banana milk and adjust sweetness if needed by adding more maple syrup.

Pour the banana milk into glasses, adding ice cubes if you'd like it cold. Set aside.

Toast the Bread: Heat a large skillet over medium heat and add olive oil. Once hot, place the slices of bread in the skillet and toast them on both sides until golden and crispy, about 2 - 3 minutes per side.

Remove the toasted bread from the skillet and set aside on plates.

Prepare the Avocado: While the bread is toasting, slice the avocado in half and remove the pit. Scoop the flesh into a bowl. Mash the avocado with a fork until smooth, leaving some chunks for texture. Add salt, black pepper, and a squeeze of lemon juice to taste.

Poach the Eggs: In a medium saucepan, fill with about 3 inches of water and bring to a gentle simmer over medium-low heat. Add white vinegar to the water to help the eggs hold their shape.

Crack one egg into a small bowl or ramekin.

Using a spoon, create a gentle whirlpool in the simmering water, then carefully slide the egg into the center of the whirlpool.

Repeat with the second egg. Poach the eggs for 3 - 4 minutes, or until the whites are set but the yolks are still runny. If you prefer firmer yolks, poach them for an additional 1 - 2 minutes.

Use a slotted spoon to remove the eggs from the water and place them on a plate lined with paper towels to drain.

Evenly spread the mashed avocado on the toasted bread slices.

Place one poached egg on top of each slice of avocado toast.

Season with additional salt and freshly ground black pepper to taste. Optionally, sprinkle with red pepper flakes for a bit of heat.

Serve the poached eggs on avocado toast with the Korean banana milk on the side.