Preheat oven to 350ºF (180ºC). Grease a 9 x 5-in. (23 x 13-cm/1.9 L) loaf pan, line bottom with strip of parchment paper with 2-in. (5-cm) overhang on either end.
In large bowl, whisk together flour, sugar, baking powder, baking soda and salt. In separate bowl, whisk eggs, buttermilk, applesauce, the 1 1/2 tsp (7 mL) lemon zest and vanilla. Pour egg mixture into dry ingredients. Mix just until incorporated. Fold in prepared strawberries. Scrape batter into prepared pan.
Bake 50 to 60 min., or until cake tester inserted in middle of loaf comes out clean. Cool loaf in pan, set on wire rack, 20 min. before using parchment overhang to lift out loaf. Cool completely on rack.
Meanwhile, to make glaze, use a whisk to blend icing sugar, lemon juice and the 1 tsp (5 mL) lemon zest. Stir in basil. Drizzle loaf with glaze. Allow glaze to set before slicing.
Wrap and store at room temperature for up to 2 days or wrap with foil and freeze for up to 2 weeks.