Roast chilis under a broiler or on a grill until outside begins to turn black and bubbly. Place chilis in a Zip-Loc bag or a container covered with plastic wrap and let cool.
Grate cheese and chop cilantro, mix together and hold for later.
In three separate bowls, place flour, beaten eggs and bread crumbs. (This is referred to as standard breading procedure: first flour, then egg, and then into the bread crumbs.)
Peel skin from chiles by wiping with a dry towel or by lightly running a paring knife over the surface of the chile.
Carefully cut a slit lengthwise in each chile and then carefully cut out the seeds.
Take the chiles one by one and stuff them full with the cheese and cilantro mixture. Place them each into the flour, then egg, and finally, into the bread crumbs. Now you have jalapeno poppers which you can hold in the refrigerator or freezer until you are ready to serve them.
Heat a large pot with vegetable oil over low-to-medium heat for frying. (The optimal temperature is 325 degrees.) Fry the jalapeno poppers for 3-5 minutes until crispy on the outside and soft in the center. Serve hot with the aioli for dipping.
To make the aioli, simply mix all ingredients and let stand until you are ready to use.