Place eggs directly from icebox into boiling water, lower to simmer and cook 7-9 minutes depending on how hard you like your yolk. Peel and set aside.
Roll each egg in flour seasoned with salt and pepper. Pull off 1/4 of the sausage meat (or an amount about equal to the size of your eggs if you are using smaller eggs) and flatten into a disk. Place an egg in the middle and fold/mold the sausage meat around the egg to completely enclose without cracks. Place in the icebox for an hour or so to firm up.
When ready to cook, set up breading stations with seasoned flour in one plate, beaten remaining egg in another, and breadcrumbs in a third. Preheat oven to 400 degrees and heat oil until shimmering and a bread crumb dropped in sizzles.
Remove eggs from icebox and move directly into hot oil. Fry for about 3 minutes, turning frequently, until browned all over. Place on a baking sheet and bake in the oven for another 10 minutes or so until nicely browned.