In a large skillet over medium heat, cook the breakfast sausage links until browned and cooked through, about 8-10 minutes. Remove from the skillet and set aside.
In the same skillet, add the bacon and cook until crispy, about 5-7 minutes. Remove and drain on paper towels.
Crack the eggs into the skillet and cook to your desired doneness (sunny-side up, over-easy, etc.), about 3-4 minutes. Season with salt and pepper. Remove and set aside.
Add the halved tomatoes to the skillet, cut side down, and cook for about 3-4 minutes until slightly charred. Remove and set aside.
Heat the baked beans in a small saucepan over low heat until warmed through, about 5 minutes.
If using black pudding, add slices to the skillet and cook for about 2-3 minutes on each side until heated through.
In another skillet, toast the bread with butter until golden brown on both sides.
To serve, arrange the sausage, bacon, eggs, tomatoes, baked beans, and black pudding (if using) on a plate. Add the toast on the side and garnish with chopped parsley if desired.