Heat the water to boiling.
Meanwhile, melt the butter in large skillet, cook the garlic and aniseed for 5 minutes, and set aside.
Put the rose petals and cactus fruit in a blender and puree until smooth and set aside.
Cut an "x" over the flat ends of the chestnuts with a knife. Toast the chestnuts in a hot cast iron skillet for 5 minutes. When the shells open, add the chestnuts to the boiling water and cook for 15 minutes. Drain the chestnuts and allow them to cool. Peel the chestnuts, add them to the rose petal mixture, and puree while adding the remaining cup of water, slowly.
Reheat the skillet with garlic butter mixture and add the rose petals puree. Simmer for 10 minutes then whisk in the honey, salt, and pepper.
Push the sauce through a sieve, into a clean pan, pressing on the solids to extract the juice and some chestnut pulp. Keep the sauce warm.
Preheat a grill or grill pan.
Drizzle the quails with olive oil and season with salt. Grill the quails until they are medium rare, about 5 minutes per side. Serve with the Rose Petal Sauce.