Aromatic rosemary-laced cake is best served warm, when the herb's flavor is at its peak and the cake is soft and tender.
Preheat oven to 350 degrees. Butter two 4 1/2-by-8 1/2-inch loaf pans, and line with parchment, leaving a 1-inch overhang on each long side. Butter parchment. Whisk together flours, baking powder, and 1 teaspoon salt.
Beat butter, sugar, rosemary, and vanilla with a mixer on medium speed until pale and fluffy, about 4 minutes. Beat in eggs and egg white, 1 at a time. Reduce speed to low. Beat in flour mixture in 2 additions, alternating with milk.
Divide batter between pans. Bake, rotating halfway through, until deep gold and a toothpick inserted in centers comes out with moist crumbs attached, 50 to 60 minutes. Brush cakes with some rosemary honey, and let cool for 10 minutes. Remove from pans, using parchment, and transfer to a wire rack. Let cool for 15 minutes more. Slice, and serve warm with more honey.