The night before, pick over the peas and discard any stones. Place in a large pot or bowl, cover with water and let soak overnight. Drain and rinse.
Combine the peas, bay leaf, cumin and 3 cups water in a saucepan over medium-high heat and bring to a rapid simmer. Cook for 5 minutes, then reduce the heat to low and cook, uncovered, until tender, 25 to 30 minutes. If the water gets low, add more to just cover the peas. Strain the peas and remove the bay leaf.
Combine the cooked peas and 1/2 teaspoon salt in a medium bowl. Let stand while you fry the olives.
Heat the oil in a medium cast-iron skillet over medium heat until hot. Add the olives and cook until fragrant and the outsides blister, 3 to 5 minutes. Pour the olives and oil over the peas. Add the parsley, parsnip, green onions and lemon juice and toss to combine. Season to taste with freshly ground black pepper and 1/2 teaspoon salt. Refrigerate until ready to serve.
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