Lightly oil a quarter sheet pan. In a small bowl, combine the onion, cornmeal, sugar, salt, and pepper. In a small saucepan, combine the stock and cream, heating the mixture to just under a boil. Whisk the dry ingredients into the saucepan of liquids, lower the heat, and cook until very thick, about 15 minutes. Remove from heat, and pour the polenta onto the oiled half sheet pan, pressing into an even layer. Chill for 4 to 6 hours or until completely firm.

When thoroughly chilled, cut the polenta into about 3-inch-size triangles. Pour the 2 cups of oil into a medium skillet set over high heat. Place a few pieces of polenta into the hot oil, frying on both sides until golden brown, 45 seconds per side. Remove from oil with a slotted spoon, and drain on a wire rack. Continue with remaining polenta. Drain the excess oil from the pan, and wipe clean. Set pan aside to sauté the asparagus.

In a small saucepan, bring the milk and cream to a low simmer. Add the goat cheese, cayenne, garlic, and mustard, whisking until combined. Using an immersion blender in the pan or transferring the sauce to the pitcher of a regular blender, process the mixture until smooth. While blending, gradually add the olive oil and the lemon juice. Salt and pepper to taste. Return the mixture to the saucepan, and simmer on low until it has thickened and reduced by a quarter, about 20 minutes.

In the polenta pan, sauté asparagus until tender. Season with salt and pepper to taste. Remove from pan.

In the same pan, fry the eggs to desired doneness. Season with salt and pepper to taste.

On a plate, arrange a couple of pieces of polenta, and top with goat cheese sauce. Pair with a few stalks of asparagus topped with a single fried egg. Continue with remaining ingredients to fill six plates. Garnish with parsley, and serve immediately.