Heat oil in a medium saucepan over medium-low heat. Add garlic and shallot and cook, stirring frequently, until softened and browned.
Add in the oats, lentils, broth, salt and pepper. Bring the mixture to a boil, then reduce heat to medium-low and cook 10-12 minutes, stirring frequently until thickened.
While the oat mixture is cooking, fill another saucepan with about 2 inches of water. Bring water to a boil, then reduce heat to low or remove from heat until mixture stops boiling. Crack eggs and gently slide eggs from shell into hot water. Turn heat off. Let eggs stand in hot water about 5 minutes or until egg white is set and yolk is still runny. When the oat mixture is done cooking, spoon it into your bowl and add the eggs, avocado and any other toppings.