In a large pot, bring split peas, turmeric, and 4 cups water to a boil. Lower heat to a simmer, partially cover, and cook 15 minutes.
Add squash, salt, sugar, and star anise. Bring to a boil, lower heat to a simmer, and cook uncovered, stirring occasionally, until squash is tender, about 15 minutes.
In a small frying pan, melt butter. When melted butter stops foaming on top, turn heat to high, add cumin seeds, and cook, stirring, until browned and fragrant, about 2 minutes. Add ginger and chiles and cook, stirring constantly, another 2 minutes. Add basil. Stir to combine and cook until basil is wilted, about 30 seconds.
Serve stew hot, with the spiced butter poured over each serving. Or stir all the spiced butter into the pot of stew before serving.
Note: Nutritional analysis is per serving.