Toast the Bagels: Slice the bagel in half. Toast the halves in a toaster or on a grill pan until golden brown and crispy. Once toasted, spread veggie cream cheese on each half.
Cook the Sausages: While the bagel halves are toasting, heat a nonstick skillet over medium heat. Add a little oil or butter and cook the sausage links for 5-7 minutes, turning occasionally until browned and fully cooked. Remove the sausages from the skillet, cover with foil to keep warm and set aside.
For the Arugula Salad: In a mixing bowl, toss arugula with olive oil, lemon juice, salt, and black pepper until evenly coated. Divide the salad between serving dishes.
Poach the Eggs: In a medium saucepan, fill with about 3 inches of water and bring to a gentle simmer over medium-low heat. Add white vinegar to the water to help the eggs hold their shape.
Crack one egg into a small bowl or ramekin. Using a spoon, create a gentle whirlpool in the simmering water, then carefully slide the egg into the center of the whirlpool.
Repeat with the remaining eggs. Poach the eggs for 3 - 4 minutes, or until the whites are set but the yolks are still runny. If you prefer firmer yolks, poach them for an additional 1 - 2 minutes.
Use a slotted spoon to remove the eggs from the water and place them on a plate lined with paper towels to drain.
Assemble the Arugula Salad: Place an egg on top of each arugula salad and season with salt and black pepper.
Pour orange juice into glasses.
Serve: Serve the bagel, arugula salad, and sausage with glasses of cold orange juice.