Using 1 tablespoon of olive oil, brush each piece of baguette on both sides.
In a large, non-stick skillet over medium heat, arrange the pieces of baguette in the pan and allow one side to toast, about 2 minutes. Flip and toast the other side of each. Remove from the pan and place each piece on a plate.
Using the same pan, add the remaining tablespoon of olive oil. Break eggs into the skillet; cover and cook for 2 to 3 minutes or until egg whites are set.
Spread ricotta mixture evenly over each slice of baguette.
Top each with a sunny side egg.
Divide baby arugula across each of the four toasts and add on top
Garnish each with extra parmesan cheese.