Heat the oil in an 8-inch skillet over medium heat. Add the onion and sauté until golden, 10 to 12 minutes. Add the garlic and 3 tablespoons of the herbs and sauté 1 minute more. Season with salt and pepper to taste.

Stir the labneh into the onion mixture and spread evenly in the pan. Cook until the labneh begins to steam and form bubbles at the edges, about 15 minutes.

Meanwhile, separate the eggs: Crack each egg in half and carefully transfer the yolk back and forth between the two halves of the shell several times over a medium bowl, tipping the shell enough to allow the egg white to slide into the bowl beneath. Place the half of the shell containing the yolk interior-side up into an empty egg carton and repeat the process with the remaining eggs and yolks. Reserve the egg whites for another use.

Using the back of a spoon, create 8 depressions in the labneh mixture and gently nestle an egg yolk in each. Cook until the yolks begin to grow firm and opaque at the edges but remain soft in the centers, 3 to 5 minutes more. Sprinkle with the remaining tablespoon of the herbs, season with salt and pepper, and serve immediately in the pan with warm pita.