Stir together the ricotta, fontina, Parmesan, lemon zest, eggs, salt, and pepper in a large bowl to combine. Slowly add the flour and stir until the dough comes together.
Bring a large pot of salted water to a gentle boil. Using a teaspoon measure, form the dough into small balls and roll in extra flour, dusting off any excess. Working in batches, add the gnudi to the boiling water and cook for about 2 minutes, until they float to the top. Once they float to the top, cook for another minute. Using a slotted spoon, drain the gnudi and transfer to a sheet tray.
Bring the water back to a boil and add the green beans. Cook for about 2 minutes, until crisp-tender. Transfer the green beans to a bowl of ice water. Drain the beans and pat dry.
Melt 2 tablespoons of butter in a large skillet over medium heat. Working in batches, add the gnudi to the pan and cook for 1 to 2 minutes per side, until golden brown. Continue cooking the gnudi, adding more butter as needed. Stir in the green beans and pesto and transfer to a serving bowl. Garnish with the pea shoots.