Remove all the cloves of garlic from the head.
Take a smallish saucepan and heat to boiling about a cup of water; add the cloves of garlic and simmer for about 1 minute- drain, peel the garlic (which should be softish and should peel easily) and set aside.
In a small saucepan, melt the butter together with the olive oil over medium heat. Reduce the temperature low, then add the peeled garlic cloves to the butter mixture; stir well.
Saute slowly on lowest heat until tender and golden, at least 20 minutes (but it can take as long as 30, depending on your stove), stirring and checking occasionally to make sure they do not burn.
Remove cloves from pan - pour any remaining butter into a wide skillet; thoroughly mash the garlic with a fork.
Heat the "garlic drippings" in the wide skillet. Swirl in the mashed garlic. Add the cooked rice and pine nuts. (If the mixture seems a little dry, you may add more butter to taste, if you like.)
Saute, stirring and tossing, until the rice is heated through and has absorbed the butter.
Season with salt and freshly ground pepper.