Lemon Drizzle Cake

Name: Lemon Drizzle Cake
Ingredients: Nonstick vegetable oil spray or room-temperature butter (for pan and knife); 1½ cups (188 g) all-purpose flour; 1 tsp. baking powder; 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt, plus more; 2–3 large lemons; 1½ cups (300 g) granulated sugar, divided; ½ cup (1 stick) unsalted butter, room temperature; 1 tsp. vanilla bean paste or vanilla extract; 2 large eggs; ½ cup whole milk; 1 cup (110 g) powdered sugar; 1–2 Tbsp. fresh lemon juice; Pinch of kosher salt