Preheat oven to 375 degrees Fahrenheit. Cut pears in half lengthwise and remove core with a melon baller or small spoon. Place pears, cut side down, in a shallow baking dish just large enough to hold them.
Pour apple juice and water over pears; drizzle with honey. Cover pan loosely with foil and bake about 35 minutes or until tender. While pears are baking, place granola in a shallow baking pan or pie plate and toast in oven 10 minutes; set aside.
When pears are done, pour baking liquid into a small saucepan and reduce over medium heat until about ¼ cup of syrup remains; set aside to cool.
Line a colander with paper towels and place over bowl to catch drips. Pour yogurt into colander and allow to drain about 30 minutes. Divide yogurt among 4 shallow bowls. Place warm pear half, cut side up, over yogurt. Top with toasted granola and drizzle with syrup. Garnish with a mint leaf, if desired.