In a 3- to 4-quart pan over high heat, bring broth and split peas to a boil; cover, reduce heat, and simmer until peas fall apart, about 50 minutes.
In a 5- to 6-quart pan over high heat, bring 2 quarts water to a boil; add ravioli. Stir occasionally until pasta is tender to bite, 4 to 6 minutes; drain.
Meanwhile, transfer split pea mixture to a blender or food processor; whirl until smooth.
Remove and discard stems from chilies; shake out and discard seeds. Wipe the 3- to 4-quart pan dry. Add chilies, oil, garlic, and cumin; stir over medium-high heat until garlic is lightly browned, about 1 minute.
Pour split pea purée into pan with chili mixture. Add spinach, tomatoes, and turmeric; stir just until steaming.
Add drained ravioli to sauce and mix gently. Spoon equally into wide bowls. Add salt and pepper to taste.