Combine apple, small rosemary sprig, the 1 teaspoon sugar, lemon, and the 1 teaspoon butter in a small saucepan. Simmer for about 5 minutes (or until chopped apple softens, if using fresh apple). Let cool and remove rosemary sprig. Transfer mixture to food processor and puree (if you used fresh apple). Combine with remaining ingredients–the heaping 3/4 cup sugar, the 1 cup butter, 3 eggs, flour, and baking powder. Mix well. (If not using fresh apple, you could do this whole thing with your mixer instead of using the food processor.)

Grease and/or line a regular-size loaf pan. (I actually do both–I grease the pan but also line the bottom with a piece of parchment cut to fit. Cakes like this have a tendency to stick, and it makes it easier to get the cake out.) Transfer mixture to the loaf pan. Place the long sprig of rosemary down the center of the batter and press lightly. Bake in a preheated 350-degree oven for 45-50 minutes or until a toothpick comes out clean.

Note: I found that I needed to tent the top with foil in the last 15 minutes of baking to prevent over-browning.

Cool in pan on a wire rack before removing the cake.