Scoop out the avocado and mash lightly. Season with salt, pepper, and lemon juice to taste. Set aside.

Heat a medium skillet over medium-high heat. Add olive oil. When hot, add sourdough slices and toast on both sides until golden brown. Remove and set aside.

Fill a medium pot with water and bring to a boil. Reduce heat to low to create a gentle simmer. Add white vinegar. Crack each egg into a small bowl and gently slide into the simmering water. Poach for 3 minutes for runny yolks or 4 minutes for jammy yolks. Remove carefully with a slotted spoon and drain on paper towels.

Plate the toasted bread, spread mashed avocado evenly over each slice. Top with whipped burrata and spoon tomato confit on top. Place poached eggs gently on the toast. Finish with flaky salt and serve immediately.