Special equipment: a cheesecloth, pasta roller and 2-inch round, square or crimped cookie cutter
For the corn puree: Heat the butter in a large saute pan over medium heat. Add the corn and cook until lightly golden brown, then add the garlic and cook for 30 seconds. Add the chile de arbol and season with salt and pepper. Remove 1/2 cup of the kernels to a bowl for the ravioli filling to let cool slightly.
Transfer the rest of the corn to a small saucepan and cover with the stock. Cook over medium heat until slightly softened, about 10 minutes. Transfer the corn to a blender with a slotted spoon, add 1/4 cup of the stock and carefully blend until the corn is smooth. Add 1/2 cup more stock to thin it slightly, then transfer the puree to the saute pan. Add more stock, if needed, to bring the puree to a sauce consistency. Stir in the creme fraiche and season with salt and pepper. Keep warm.
For the ravioli: Place a fine mesh strainer over a bowl and line it with cheesecloth. Place the ricotta in the strainer and drain for 4 hours.
Whisk together 3 of the eggs, the yolk and some salt and pepper in a small bowl. Put the flour in another bowl, make a well in the center, add the egg mixture in the center and mix the flour into the eggs with a fork until combined. Transfer the dough to a lightly floured surface and knead until smooth. Wrap in plastic and refrigerate for at least 1 hour and up to 24 hours.
Combine the drained ricotta, Parmesan, the reserved sauteed corn and 1 egg in a bowl and season with salt and pepper.
Divide the dough into quarters and roll thinly in a pasta machine to 1/8-inch thickness. Whisk the remaining 2 eggs together with a tablespoon of water. Dust the counter and dough with flour and lay out 2 sheets of the pasta. Brush the top surface of dough with the egg wash. Distribute 1-tablespoon mounds of filling about 2 inches apart on the 2 sheets of dough. Top with the remaining 2 sheets of dough. Using your fingers, gently press out the air pockets around each mound of filling and form a seal. Use a crimper or cookie cutter to cut each ravioli into squares or circles. Check to make sure the crimped edges are well sealed before cooking. If making the ravioli in advance, dust with cornmeal to prevent them from sticking.
For the sauteed cherry tomato sauce: Heat the oil in a large saute pan over medium heat. Add the tomatoes and cook until they begin to soften, about 5 minutes. Add the garlic and salt and pepper and cook until the juices release and then thicken slightly, about 5 minutes. Season with additional salt and pepper and stir in the basil.
For the anchovy breadcrumbs: Heat the oil in a small saute pan over low heat, add the anchovies and cook until they are melted into the oil, about 1 minute. Add the breadcrumbs and cook until lightly golden brown, then season with salt and pepper.
To serve: Bring 4 quarts of salted water to a boil. Cook the ravioli, in batches, until they float, about 2 minutes. Lift the ravioli from the water with a large strainer or slotted spoon and toss in the cherry tomato sauce to coat.
Ladle some of the corn puree into 4 large shallow bowls. Top with 3 large ravioli in sauce, grate fresh Parmesan over and sprinkle with anchovy breadcrumbs.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.