Thinly slice 1 garlic clove, and set aside. Gently crush remaining clove, and rub over one side of each of the bread slices. Brush both sides of bread with 1 tablespoon olive oil. Toast slices on a grill or in a skillet over medium-high heat until golden and crisp on both sides. Transfer to a serving platter, and set aside.
Heat remaining tablespoon olive oil in a medium skillet over medium-high heat. Add reserved garlic and artichoke hearts. Saute until golden, 3 to 4 minutes. Set aside.
Season ricotta cheese with salt and pepper; spread about 2 tablespoons of mixture on each slice of bread. Top with sauteed garlic and artichokes. Season again with salt and pepper. Garnish with shaved Parmesan cheese, and drizzle with olive oil.