Preheat your oven to 325°F (160°C). Grease and flour (using GF flour) a 9×5 inch loaf pan.
In a medium bowl, whisk together the gluten-free flour blend, baking powder, and salt. Set aside.
In a large bowl, beat the softened butter and granulated sugar with an electric mixer until light and fluffy, about 3 minutes.
Beat in the eggs one at a time, mixing well after each addition.
Mix in the lemon zest, lemon juice, and vanilla extract until just combined.
Gradually add the dry ingredients to the wet ingredients, alternating with the milk, beginning and ending with the flour mixture. Mix on low speed until just combined; do not overmix.
Pour about two-thirds of the batter into the prepared loaf pan. Drizzle the strawberry puree over the batter. Pour the remaining batter on top.
Use a knife or skewer to gently swirl the puree through the batter 2 or 3 times to create a marbled effect.
Bake for 60 to 75 minutes, or until a wooden skewer inserted into the center comes out clean. If the top browns too quickly, loosely tent it with foil after 45 minutes.
Let the cake cool in the pan for 15 minutes before inverting it onto a wire rack to cool completely.
While the cake cools, prepare the glaze: Whisk together the powdered sugar and 2 tablespoons of lemon juice until smooth. Add more lemon juice, 1 teaspoon at a time, if needed to reach a thick but pourable consistency.
Drizzle the lemon glaze over the cooled cake before slicing and serving.
Notes
If your GF flour blend does not contain xanthan gum, add 1/2 teaspoon to the dry ingredients.
For a stronger strawberry flavor, reduce the milk slightly and use the strawberry puree in place of some of the liquid.
This cake keeps well wrapped tightly at room temperature for up to 3 days.