Slice the bacon into 1/2-inch chunks. Add to a large soup pot and cook over medium-high heat to render the fat and get crispy on all sides, about 8 minutes total. The more brown the better; just don't burn them. They are perfect when they are more chewy than juicy.
Remove bacon chunks and set aside on a paper towel lined plate. Pour off all but 2 to 3 tablespoons of fat from the stock pot. Add the onion, carrot and celery with a pinch of salt and pepper and saute until onions are just translucent, about 6 to 8 minutes. Stir in the garlic and cumin and let cook another minute before adding the split peas and stock. Cover and bring to a boil. Reduce the heat and simmer until the peas are al dente (cooked through, but slightly firm and whole), about 20 minutes. Cool for 5 minutes.
Ladle out about 3 cups of the peas and carefully blitz the remaining soup using an immersion blender or countertop blender until creamy. If using a countertop blender be sure to only fill it about 1/3 the way up and start on a slow speed, then raise to a higher speed. This method will take a bit longer due to the need to blitz in batches. Pour the soup back into the pot. Return the 3 cups of peas to the soup and stir to combine and heat through. Season with salt and pepper, to taste. To serve, ladle the soup into bowls and top with bacon, tomato and a squeeze of lime.