1. In a 4- to 6-quart pan over high heat, bring 5 cups water to a boil. Rinse split peas and remove debris. Add split peas, cloves, and cinnamon stick to boiling water. Reduce heat, cover, and simmer, stirring occasionally, until peas are very soft and starting to break down, 1 to 1 1/2 hours (mixture should be soupy). If peas begin to stick before they're done, add more water 1/2 cup at a time. Remove and discard cloves and cinnamon stick if desired.
2. Meanwhile, in a 3- to 4-quart pan over high heat, bring 2 1/2 cups water to a boil. Add rice, reduce heat to a simmer, cover, and simmer until rice is tender to bite, about 20 minutes.
3. In a 1- to 1 1/2-quart pan over medium heat, melt butter. Stir in cumin, turmeric, mustard seeds, cayenne, coriander, and ginger and cook until fragrant, 1 to 2 minutes. Stir spice mixture into cooked split peas and add salt to taste.
4. Divide cooked rice evenly among four to six wide, shallow bowls and spoon dal equally onto rice. Add mango and yogurt on the side.