Adjust oven rack to middle position and heat oven to 350 degrees.
Grease 9 by 5-inch loaf pan with 1 tablespoon softened butter; dust with 1 tablespoon cake flour, tapping out excess. For this recipe, I actually used mini loaf pans: 5.5 by 3-inch.
In medium bowl, whisk together flour, baking powder, and salt; set aside.
Toss 1 tablespoon flour mixture and poppy seeds in small bowl, set aside.
In glass measuring cup or microwave-safe bowl, microwave butter, covered with plastic wrap, at full power until melted, 1 to 2 minutes. (Alternatively, melt butter in small saucepan over medium heat.)
Whisk melted butter thoroughly to re-incorporate any separated milk solids.
In a food processor, process sugar and zest until combined, about five 1-second pulses.
Add lemon juice, eggs, and vanilla; process until combined, about 5 seconds.
With machine running, add melted butter through feed tube in steady stream (this should take about 20 seconds).
Transfer mixture to large bowl.
Sift flour mixture over eggs in three steps, whisking gently after each addition until just combined.
Fold poppy seed mixture into batter after flour is incorporated.
Pour batter into prepared pans and bake 15 minutes.
Reduce oven temperature to 325 degrees and continue to bake until deep golden brown and skewer inserted in center comes out clean, about 35 minutes, rotating pan halfway through baking time.
Cool in pan for 10 minutes, then turn onto wire rack.
While cake is cooling in pan, make lemon glaze (if using). Bring sugar and lemon juice to boil in small nonreactive saucepan, stirring occasionally to dissolve sugar.
Reduce heat to low and simmer until thickened slightly, about 2 minutes.
Brush on or pour lemon glaze. Cool to room temperature, at least 1 hour. (Cooled cake can be wrapped tightly in plastic wrap and stored at room temperature for up to 5 days.)