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Preheat the oven to 350°F. Lightly grease an 8 1/2” x 4 1/2” loaf pan.
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To make the bread: In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
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In a separate medium bowl, mix the baking sugar alternative with the lemon zest. Rub together with your fingers to thoroughly combine.
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Add the vegetable oil, eggs, lemon juice, lemon oil, and vanilla to the sugar alternative mixture and whisk until smooth.
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Add the flour mixture in three additions alternately with the milk, starting and ending with the flour mixture and mixing just until smooth. Stir in the poppy seeds.
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Transfer the batter to the prepared pan and smooth the top.
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Bake the bread for 45 to 50 minutes, until a toothpick inserted into the center comes out clean. Tent the loaf with aluminum foil after 35 minutes to prevent over-browning.
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To make the glaze: While the loaf is baking, combine the baking sugar alternative and lemon juice. Stir to combine and then heat for 5 to 10 seconds in the microwave to dissolve the sugar alternative.
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Remove the bread from the oven and cool it in the pan for 10 minutes before turning it out onto a rack.
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Brush the glaze all over the warm loaf, both top and sides. Let it sink in, then brush on more glaze, continuing until all the glaze is used.
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Store the bread at room temperature, well wrapped, for several days; freeze for longer storage.