Peel, core and dice your pears and apples. You want about 2-1/2 cups of diced fruit—we used 2 pears and 2 apples, and had some pieces left over for snacking on. Toss fruit in a bowl with 2 tablespoons of lemon juice and set aside.
Preheat oven to 350ºF. In a large bowl, mix the flour, baking soda, baking powder, salt, spice and white sugar. Add the brown sugar—break up any lumps with your fingers—and then stir everything together lightly with a fork.
In a small bowl, beat the eggs for a minute or so until they begin to turn pale, then add the sour cream, vanilla, the half & half, milk or buttermilk, and the fresh rosemary and lemon zest, and stir together, then add the butter and olive oil and stir all together well.
Pour the egg mixture into the dry ingredients and mix together, using a big spoon. Finally, fold in the apples and pears, just until everything is even and uniform.
Prepare your bundt pan now—brush it thoroughly with oil. Then immediately spoon in the batter. Level the top and put the pan in the hot oven.
Set a timer for 55 minutes, but keep an eye on it in the last couple of minutes. The cake is ready when a tester inserted in the center comes out clean and the cake is just pulling away from the sides.
Cool in the pan on a rack for 15 or 20 minutes, then loosen the edges with a table knife, turn it out onto a platter, and cool completely.