Bring a large pot of water to a boil, add the sea salt, and cook the chickpea spaghetti until just al dente according to package directions.
While the pasta cooks, add the diced pancetta to a cold skillet and turn the heat to medium, rendering the fat until it becomes crispy.
Add the finely diced chicken breast and the smashed garlic clove to the skillet, sautéing until the chicken is golden and cooked through.
In a small mixing bowl, whisk together the whole egg, egg yolk, grated Pecorino Romano, and freshly cracked black pepper until the mixture is smooth.
Reserve 0.25 cup of the starchy pasta cooking water, then drain the spaghetti and add it directly to the skillet with the chicken and pancetta.
Remove the skillet from the heat immediately to prevent the eggs from scrambling, then quickly stir in the egg mixture and the reserved pasta water.
Toss the pasta vigorously for 1 minute until the sauce emulsifies into a glossy, creamy coating that clings to every strand.