How to Make It
In a large heavy pot, brown the ham hock in the oil over medium high heat, turning occasionally, until golden, about 8 minutes. Stir the onions, garlic, and 1/2 teaspoon each salt and pepper and cook, stirring occasionally, until golden, 8 to 10 minutes. Stir in the carrots, celery, stock, and split peas and bring to a simmer. Cook, stirring occasionally, until the split peas are very soft and falling apart, about 1 1/2 hours. Season with salt and pepper to taste.
While the soup cooks, in a small saucepan, bring the vinegar, water, sugar and 1/2 teaspoon salt to a simmer. Remove the vinegar mixture from the heat and stir in the shallots. Let stand 30 minutes then drain.