Prepare the Bread Position an oven rack 4-6 inches from the broiler element and set the broiler to HIGH. Arrange the bread slices on a baking sheet. Lightly brush one side of each slice with olive oil.
Broil the Toast Place the baking sheet under the broiler. Toast for 1-2 minutes until the tops are golden and the edges are crisp. Remove, flip the slices, and broil for another 60-90 seconds. Set the finished toast aside.
Heat the Poaching Water While the bread broils, fill the saucepan with about 3 inches (7.5 cm) of water. Add the white vinegar, which helps the egg whites congeal. Bring the water to a gentle simmer, with small, consistent bubbles rising from the bottom. Avoid a full rolling boil.
Poach the Eggs Crack one egg into a small bowl. Create a gentle vortex in the water with a spoon and carefully slide the egg into the center. Cook for 3-4 minutes, or until the whites are fully opaque but the yolk remains soft and runny. Gently lift the egg out with a slotted spoon, allowing excess water to drain. Repeat with the remaining eggs.
Season the Avocado Halve the avocado, remove the pit, and scoop the flesh into a bowl. Add the smoked paprika and a few grinds of black pepper. Gently mash with a fork, leaving some texture.
Assemble the Toast Spread a generous layer of low-sodium cottage cheese over each slice of broiled bread. Top with a quarter of the seasoned avocado mash.
Garnish and Serve Carefully place a warm poached egg on top of the avocado. Finish each toast with a ½ teaspoon drizzle of chili crunch and a sprinkle of fresh chives. Serve immediately.