Place a large non-stick skillet over medium heat and add the pork sausage links, cooking for 8-10 minutes until browned and cooked through.
While the sausages cook, place the baked beans in a small saucepan over low heat, stirring occasionally until warmed through.
Move the sausages to one side of the skillet and add the ghee to the empty space; add the sliced cremini mushrooms and the tomato half, cut-side down.
Sauté the mushrooms until they are tender and the tomato is slightly charred, about 4-5 minutes, then remove them and the sausages from the pan and keep warm.
Crack the eggs into the same skillet and fry until the whites are set but the yolks remain runny, about 3 minutes.
Arrange the sausages, eggs, mushrooms, tomato, and beans on a large plate, seasoning everything with sea salt and black pepper before serving.