Preheat the oven to 425°F. Grease and line a 9×5-inch loaf pan with parchment paper.
In a large bowl, whisk flour, cornmeal, baking powder, baking soda, and salt. Stir in rosemary.
In another bowl, whisk eggs, sugar, buttermilk, and olive oil.
Combine wet and dry ingredients, stirring just until mixed.
Spread batter into prepared pan.
Bake for 40–45 minutes until a toothpick inserted in the center comes out clean.
Cool completely before removing from the pan.
Beat butter and lingonberry jam until smooth.
Slice loaf and serve with butter.