To begin, place 4 eggs in a saucepan of cold water. Bring to a gentle boil, cook for 6 minutes for a soft centre or 8 minutes for a firmer yolk. Transfer immediately to iced water to stop cooking. Peel carefully once cooled. Transition to preparing sausage mixture.
In a large bowl, combine sausage meat with mustard, thyme, garlic, nutmeg, salt, and pepper. Mix lightly with your hands until evenly combined. Do not overwork to keep the meat tender. Move to shaping portions.
Divide the sausage meat into 4 equal portions. Roll each into a ball, then flatten into a thin round patty large enough to wrap around an egg. Prepare the dredging station next.
Place flour on one plate, beat 2 eggs in a shallow bowl, and spread breadcrumbs on another plate. This three-stage coating ensures crisp results. Transition to wrapping eggs.
Roll each peeled egg in flour, then place in the centre of a sausage patty. Carefully shape the sausage meat around the egg, sealing any cracks with damp hands. Coat all 4 eggs. Continue to coating with crumbs.
Dip each sausage covered egg into beaten egg, then roll in breadcrumbs, pressing lightly to secure an even coat. For extra crunch, repeat the egg wash and breadcrumb coating. Transition to frying.
Pour oil into a deep pan or fryer to a depth of about 7–8 cm. Heat to 170°C. Test with a cube of bread: it should brown in 40 seconds. Move to frying.
Lower the coated eggs gently into the hot oil. Fry in batches for 6–8 minutes, turning occasionally, until the sausage meat is fully cooked and the coating is deep golden. Transition to draining.
Remove the Scotch eggs with a slotted spoon and drain on kitchen paper. Rest for 5 minutes to allow the crust to firm up. Transition to serving.
Slice in half and serve warm with mustard or brown sauce. Alternatively, chill and pack for a picnic. Presentation tip: place halved Scotch eggs on a wooden board with pickles for a pub style serving.