For the pasta: Mound the "00" flour on a clean work surface and make a well in the center. Crack the eggs into the well and beat with a fork. Add the olive oil and season with salt and pepper. Slowly work the flour from the edges of well into center until a dough ball starts to form. Knead for 3 to 5 minutes, until very smooth. Wrap in plastic and let rest at room temperature for 30 min.
Divide the dough into four pieces and cover with a damp towel. Using a pasta roller set to the thickest (widest) setting, roll one piece of dough out into a sheet. Fold the sheet in half and pass it through the roller again on the same setting. Reduce the setting and repeat, rolling and folding the dough and passing it twice through the machine before going to the next setting. Continue in this manner until the thinnest setting has been used. Repeat with rest of the dough.
Let rest on a baking rack for 10 to 15 minutes, until the moisture is reduced by about half.
Preheat the oven to 400 degrees F.
For the cheese sauce: Add the butter and all-purpose flour to a heavy-bottomed pot over medium heat. Cook, stirring continuously, until blond and smooth. Whisk in the milk and bring to a boil. Add the mustard, hot sauce and cheeses, slowly at first; cook, whisking, until smooth and combined. Add salt and pepper to taste.
For the green chile puree: To a blender, add the olive oil and the sherry vinegar, garlic, shallot and chiles. Blend until smooth. Season with salt and pepper.
To assemble dish: Bring 4 cups salted water to a boil. Cut the pasta sheets to fit a buttered 10-inch square casserole dish. In batches, cook the pasta sheets for 1 minute in the boiling water; immediately submerge in an ice bath to stop cooking.
Spread a ladleful of cheese sauce in the bottom of the casserole dish; arrange pasta sheets on top to fit the dish. Ladle in more cheese sauce, just to cover, then liberally spread with green chile puree. Cover with more pasta sheets. Repeat the layers all the way to the top of the casserole dish. Sprinkle the Parmesan on top.
Bake until golden brown and delicious, and the center has reached 160 degrees F, about 15 minutes.