Bring water with vinegar to a gentle boil.
Carefully break one egg into a fine-mesh strainer, allowing the thin, watery part of the egg white to pass through the mesh while keeping the egg yolk and thicker egg white in the strainer.
Carefully slide the eggs from the strainer into the gently simmering water (you can dip the strainer with the egg into the water, gently release the egg, and take the strainer out). Let the eggs poach in the simmering water for about 3-4 minutes, or until the egg whites are fully set, and the yolk is still slightly runny. You can adjust the cooking time based on your preference for yolk consistency.
Cut the avocado in half and remove the pit. Carefully make lengthwise slices into the avocado flesh with the knife while still inside the skin. Once you've sliced the avocado, take a spoon and gently scoop out the avocado flesh by sliding the spoon between the scored flesh and the skin. Spread cream cheese evenly over whole-grain bread and add avocado slices. Place the poached eggs on top of the avocado slices.