Place the Parmesan in a food processor. Pulse until finely ground. Add the panko bread crumbs to the bowl and pulse a few more times so the cheese and crumbs are uniform. Add ground pepper to taste. Pour the mixture onto a plate. Wipe out the bowl of the food processor.
Put the goat cheese in a small bowl. Mince the garlic. Sprinkle the 1/4 teaspoon coarse salt over the minced garlic and smash the mixture together with a fork so that it come together a little bit. Add the garlic to the bowl with the goat cheese and add salt and pepper to taste. Stir the mixture together until smooth and well blended. Use your hands to form the goat cheese mixture into a round ball. Roll the ball in the Parmesan-panko mixture until well coated, pressing gently. Cover in plastic wrap and put it in the fridge.
For the basil oil, bring a small pot of water to a boil. Add the basil leaves to the pot and boil for 30 seconds. Drain and rinse immediately with cold water. Gently dry the basil leaves with a paper towel to remove all of the excess water. Add the basil leaves and the garlic to the food processor. Pulse until finely minced. Scrape down the sides of the bowl. With the food processor running, add the oil through the feed tube in a steady stream. Continue processing until the mixture is well blended and the oil is green. Strain the oil mixture through a fine mesh sieve onto a medium size serving plate. Place the ball of goat cheese in the center of the basil oil. Garnish with additional fresh basil if you want. Serve with baguette slices.