Step 1Fill a large saute pan with water and bring to a boil. Adjust the heat to keep the water at a steady simmer. Break each egg into a small saucer or ramekin and slip the eggs into the water one at a time. Simmer until the whites of the eggs are done but the yolks are still runny, about 3 minutes. Lift each egg out of the water with a slotted spatula into a shallow glass dish filled with cold water. Refrigerate the eggs in the water until you're ready to assemble.
Step 2Bring a small saucepan of water to a boil over high heat, then adjust the heat to maintain a steady simmer. Add the peas and salt and cook about 2 minutes until tender yet crisp. Use a slotted spoon to remove the peas from the saucepan to a bowl of ice water fitted with a strainer. Once the peas are chilled, lift them out of the ice water in the strainer and gently pat dry on paper towels. Repeat the same process with the carrot slices, cooking them for 1 1/2 minutes. Then the haricots verts, cooking them 2 minutes. Cook the asparagus tips about 2 minutes, until tender. Refrigerate the vegetables until you are ready to assemble the gelee.
Step 3To make the stock, add the leeks, carrots and celery to a large heavy-bottomed saucepan with 2 tablespoons water. Sweat the vegetables over medium low heat in the water until slightly softened, about 10 minutes, stirring occasionally.
Step 4Stir in 4 cups water, the peppercorns, bay leaf, parsley, fennel and thyme. Bring to a boil over high heat, then reduce the heat and simmer 30 minutes. Skim off foam, if necessary.
Step 5Remove the stock from the heat and strain through a cheesecloth-lined, fine-mesh strainer. Gently press the vegetables to extract the liquid. Discard the vegetables. You should have about 2 cups stock. Place the stock back in the pan over high heat and reduce to 1 1/3 cups.
Step 6Place the wine in a small bowl and gently sprinkle the gelatin over, allowing it to moisten in the wine. Stir the wine-soaked gelatin into the reduced stock until it is dissolved, then stir in the lemon juice and salt. Chill the gelatin in a metal bowl over another bowl of ice water until it just begins to thicken but is not yet set. Immediately remove the gelatin from the ice bath.
Step 7Stir the blanched peas, carrots and haricots verts into the thickening gelatin; they should be suspended in it. Spoon about one-fourth cup of the gelatin mixture into the bottom of each of four lightly oiled 6-ounce ramekins. Press 3 or 4 chervil leaves into the gelatin of each ramekin. Then put a well-drained poached egg on top. Cover each egg with the remaining gelatin-vegetable mixture.
Step 8Press a blanched asparagus tip onto the top of each ramekin so the asparagus is covered in gelee. Press a few chervil leaves into the gelatin over the top of each ramekin.
Step 9Put the ramekins on a tray and chill until set, at least 2 hours or overnight. To unmold, run a knife around the edge of each ramekin. Put the bottom of each ramekin under warm water and shake to release from the dish. Turn upside down onto a plate or platter to serve.