Bring a medium saucepan of water to a boil over high heat. Carefully lower 8 of the eggs into the boiling water one-by-one with a spoon and cook for 6 minutes. Prepare a bowl of ice water, then transfer the eggs to the bowl to stop the cooking process; let sit for at least 5 minutes. Carefully peel the eggs and set aside.
Meanwhile, fill a large Dutch oven or heavy pot halfway with canola oil and heat over medium-high heat to 350 degrees F.
Combine the sausage, 1/4 cup of the mustard and half the parsley in a medium bowl and mix well. Divide the sausage mixture into 8 even balls. Flatten each ball into an oval in your hand, put a peeled egg in the middle of each and wrap the sausage mixture around to completely cover.
Put the flour in a shallow dish. Crack the remaining egg into another shallow dish, add the remaining 1/4 cup mustard and beat with a fork until well combined. Put the breadcrumbs in a third shallow dish. Dip the sausage-covered eggs first in the flour, then in the egg mixture, then in the breadcrumbs to coat.
Carefully lower the coated eggs one-by-one into the hot oil with a slotted spoon (the oil temperature will drop to around 300 degrees F). Cook, adjusting the heat as needed to remain around 300 degrees F and turning the eggs to ensure even cooking, until golden brown all over and the sausage is cooked through, about 10 minutes. Transfer the eggs to a paper-towel-lined plate. Sprinkle with salt, pepper and the remaining parsley and gently roll the eggs a few times to coat. Cut each egg in half lengthwise and serve immediately with extra mustard.