Fill a pot halfway with water and stir in the vinegar. Bring the water to a low simmer.
Poach the eggs: Crack the eggs into a bowl. Gently place the eggs into the simmering water. You can poach multiple eggs at once, being careful not to overcrowd the pan. Cook the eggs in the water for 3-4 minutes. Remove the eggs with a slotted spoon onto paper towels. Season with salt and pepper to taste.
Prepare the tea. Stir in the vanilla and condensed milk.
Drizzle the oil onto the inside of each slice of bread. Layer with arugula, avocado seasoned with salt and pepper, poached eggs, and top piece of bread.