Combine water, split peas, garlic and chilli in a medium, heavy-based saucepan. Bring to the boil. Reduce the heat to low, partially cover and simmer, stirring occasionally, until split peas are tender and most of the liquid has been absorbed, 40 to 50 minutes. (Add more water during cooking, if necessary. If the mixture seems too soupy at the end of cooking, simmer, uncovered, stirring constantly, for a few minutes, or until the mixture has the consistency of very thick split pea soup.) Let cool slightly.
Transfer split pea mixture to a food processor. Add lemon juice, 2 tablespoons of the oil and cumin. Process until smooth. To serve, spread the puree in a shallow serving dish. Drizzle with the remaining oil. Sprinkle with the red onion and mint. The spread will keep, covered, in the refrigerator for up to 4 days.