Gently rinse the morel mushrooms to remove visible dirt. Remove the stems with kitchen scissors or a sharp knife. Trim any discolored or dirty bits off and finely chop the remaining pieces of stem. Set aside.
Fill a large bowl with cold water and add 1 Tbsp salt. Stir well to dissolve the salt. Add the morels and soak for 20 - 30 minutes, gently plunging them under the surface of the water from time to time. This will help to dislodge any grit or debris from the honeycomb structure of the morels and from the interior. (The salt will also flush out any annoying little creepy-crawlers that may have taken up residence.)
Drain the morels in a colander and gently rinse them again. Place the clean morels on paper towels to dry for a few minutes.
In the meanwhile, carefully dice the cheese into small, 1/8-inch cubes and place them into a small bowl.
Heat the olive oil in a small pan over medium-low heat. Add the chopped garlic, serrano chile and morel stems. Saute briefly until the garlic and chile are softened, about 3 or 4 minutes. Add the crushed chile pepper, stir briefly, and remove from the heat. Allow to cool for a minute or two and then add the sauteed ingredients and chives to the diced cheese. Mix briefly to combine the ingredients. Add black pepper to taste.
Cut a slit in the side of each morel mushroom and fill with as much of the cheese mixture as it will hold. Repeat until all of the morels are filled and set them aside.
Separate the egg yolk and white into very clean small bowls. Using an electric mixer (or whisk by hand if you're a masochist), beat the egg yolk until it becomes creamy and light yellow in color. Wash the beater (it must be perfectly clean!) and beat the egg whites until soft peaks form. Gently fold the beaten yolk into the white until it is completely incorporated. The resulting mixture should be light and foamy and pale yellow.
Heat the vegetable oil in a medium-sized pan over medium-high heat. While the oil is heating up, dredge the cheese-filled morels in the flour. Test the temperature of the oil by flicking a drop of the egg mixture into the pan. If it sizzles up immediately, the oil is hot and ready.
Working very quickly, plunge each flour-dusted morel into the egg mixture, making sure it is completely covered, and gently drop it into the hot oil. Repeat with more of the morels, but do not crowd the pan. When the bottom is well-browned, turn each morel with tongs. Turn again to brown all sides as necessary. Remove the cooked morels to a paper towel-lined plate and keep warm. Repeat, cooking the remaining filled morels in batches.
Sprinkle the morels generously with the sea salt and serve immediately while piping hot.