In a large stockpot or dutch oven, over medium heat, cook bacon until crispy, 8 minutes. Transfer to a paper towel-lined plate and let cool, then crumble.
Add onion, carrot, and garlic to bacon fat and cook until tender and golden, 6 to 8 minutes. Season generously with salt and pepper.
Add broth and split peas and let simmer, covered, until split peas are tender, 35 to 40 minutes.