Blend the beets with the gherkins, the sandwich bread moistened with 1 tablespoon of vinegar, 2 teaspoons of drained capers, salt, and pepper until you obtain a smooth sauce.
Warm the piadinas in a skillet, stacking and turning them occasionally. In another skillet, cook the eggs sunny-side up with a drizzle of olive oil and a pinch of salt.
Spread the beet sauce over the piadinas, gently place the sunny-side-up eggs on top, and serve accompanied by the plain yogurt and fresh basil.