Allow butter and eggs to stand at room temperature for 30 minutes. Grease and lightly flour two 8x4x2-inch loaf pans; set aside. In a medium bowl, combine all-purpose flour, cake flour, and baking powder; set aside.
In a large bowl, beat butter with an electric mixer on medium to high speed for 30 seconds or until softened. Gradually add sugar, 2 tablespoons at a time, beating on medium speed about 6 minutes or until very light and fluffy. Add eggs, one at a time, beating on low to medium speed for 1 minute after each addition and scraping bowl frequently. (Batter may look slightly curdled.) Gradually add flour mixture, beating on low speed just until combined. Gently stir in snipped basil and tarragon.
Pour batter into prepared pans. Bake in a 325 degree F oven for 45 to 50 minutes or until wooden toothpick inserted in centers comes out clean. Cool in pans for 10 minutes. Remove from pans, and cool on wire racks.
To serve, if you like, top each slice with a scoop of frozen lemon yogurt.