In a large skillet with a tightly fitting top, boil rice in several cups of water for ten minutes. Drain and pat skillet dry. Add butter and oil, coating entire bottom of skillet. Add one thin layer of rice to the bottom, pressing firmly.
Mix remaining rice with yogurt, salt, saffron liquid, mint, dill, pomegranate, and dates; combine well. Pile on top of rice layer in skillet. Cover with lid, using a towel to seal any air holes if necessary (take care this does not come near flames). Cook on medium for 20 minutes. Do not remove lid! Decrease heat to low and cook 20 more minutes. Remove from heat and cool for five minutes. Loosen rice around the edges and bottom and carefully flip onto a serving plate.
Garnish with more herbs, fruits, and edible flowers.