In a large saucepan, combine the split peas and water and bring to a boil over high heat. Reduce heat to maintain a steady simmer and skim off any foam. Add the garlic to the pan, cover partially, and simmer, stirring occasionally, until the peas are very tender and broken, about 25 minutes.
Remove pan from heat and smash the garlic in the saucepan into a paste. Stir the mixture vigorously until almost smooth. (If you prefer a smoother texture, transfer the mixture to a food processor or a blender and puree.) Let cool to room temperature.
Stir in the tahini, lemon juice, oil, and rose spice mix and season to taste with salt. Transfer to a serving dish, garnish with rose petals, and serve with crackers, pita chips, or crudités. The hummus can be refrigerated for up to 1 week in an airtight container.