Prepare the water for poaching: Fill a medium saucepan with about 3 inches of water. Add white vinegar and bring to a gentle simmer over medium heat.
Toast the bread: While water heats, toast the whole grain bread slices until golden brown and crispy.
Prepare the avocado: Cut the avocado in half, remove the pit, and scoop flesh into a bowl. Add lemon juice, salt, and pepper. Mash with a fork until smooth but still slightly chunky.
Poach the eggs: Crack each egg into a small bowl. Create a gentle whirlpool in the simmering water with a spoon, then slowly lower one egg into the center. Repeat with the second egg. Poach for 3-4 minutes for runny yolks.
Assemble: Spread the mashed avocado evenly on the toasted bread. Drizzle with olive oil.
Finish: Using a slotted spoon, carefully remove poached eggs and place one on each toast. Sprinkle with everything bagel seasoning, red pepper flakes, and fresh herbs.