Bring a large pot of salted water to a boil. Cook the paccheri for 1 minute less than the package directions. Reserve 1/2 cup pasta water, then drain. Rinse the pasta thoroughly with cold water after draining.
Combine the ricotta with 1/2 cup of the pesto and 2 cups of fontina, then mix well. Season with salt and pepper. Transfer to a piping bag or resealable bag with the corner snipped off. Pipe the mixture into each paccheri. (This doesn't need to be perfect. If a paccheri is very torn or broken, do not use.) Stand each filled paccheri upright in a 10-inch springform pan until it is packed tightly.
Thin the alfredo sauce with the reserved pasta water in a bowl, then pour it into the pan over the filled paccheri, spreading evenly. Sprinkle with the remaining 2 cups fontina cheese.
Bake until the mixture is bubbly and the cheese on top is melted, 35 to 40 minutes. Remove from the oven and let sit for 5 minutes. Drizzle with the rest of the pesto and garnish with the fresh basil. Remove the springform side, then slice and serve.