In a large skillet, heat oil over medium heat. Add sausage; cook and stir until lightly browned, 2-3 minutes. Add zucchini; cook and stir until tender, 4-5 minutes longer. Remove from pan; keep warm.
Meanwhile, in a large saucepan, bring water to a boil. Slowly stir in grits. Reduce heat to medium-low; cook, covered, until thickened, stirring occasionally, about 5 minutes. Stir in beans and cheese until blended. Remove from heat.
Wipe skillet clean; coat with cooking spray and place over medium heat. In batches, break eggs, 1 at a time, into pan. Immediately reduce heat to low; cook until whites are completely set and yolks begin to thicken but are not hard, about 5 minutes.
To serve, divide grits mixture among 6 bowls. Top with chorizo mixture, eggs and, if desired, pico de gallo and cilantro.
