Heat a skillet over medium heat with a drizzle of olive oil. Toast sourdough bread slices until golden brown on both sides. Remove and set aside.
Bring a small saucepan of water to a boil. Add distilled white vinegar, then reduce to a steady simmer.
Crack each egg into separate ramekins. Create a gentle vortex in the simmering water using a spoon. Carefully tilt each egg into the water. Poach for about 2 minutes or until eggs reach desired doneness. Remove with a slotted spoon and drain on paper towels. Set aside.
In a food processor, combine feta cheese and olive brine. Process until smooth while slowly adding 2-3 tablespoon olive oil to create whipped feta. Set aside.
Toss arugula in a small bowl with a drizzle of olive oil and flaky salt. Set aside.
To assemble, spread 2 tablespoon whipped feta evenly over each slice of toast. Top with arugula, then tomato confit, and finally place the poached eggs on top.
Garnish with pickled red onions, flaky salt, and freshly ground black pepper. Serve immediately.