Heat olive oil in a skillet over medium heat. Cook and stir chicken sausage and chorizo sausage in the hot oil until browned and cooked through, about 10 minutes. Drain excess grease.
Stir sweet potato, garlic powder, cayenne pepper, salt, and pepper into sausage mixture; add chicken broth and simmer, adding more chicken broth if mixture gets too dry, until sweet potato is tender, 10 to 15 minutes. Mix zucchini and spinach into sweet potato-sausage mixture and simmer until zucchini is tender, 5 to 10 minutes. Drain excess liquid.
Fill a large saucepan with 2 to 3 inches of water and bring to a boil. Reduce the heat to medium-low and keep the water at a gentle simmer. Crack an egg into a small bowl then gently slip the egg into the simmering water, holding the bowl just above the surface of the water. Poach the egg until the whites are firm and the yolks have thickened but are not hard, 2 1/2 to 3 minutes. Remove egg from the water with a slotted spoon.
Top sweet potato-sausage mixture with poached egg.
