Preheat your oven to 325°F (165°C) with a rack in the center position. Grease a 9x5-inch loaf pan with butter, line with a parchment paper sling, then lightly flour the inside and tap out any excess.
In a medium bowl, whisk together the flour, baking powder, and salt until evenly combined. Set aside.
Zest 3–4 lemons using a microplane to yield 3 tablespoons of packed zest, avoiding the bitter white pith. Juice the same lemons to yield 3 tablespoons for the batter and 1/4 cup for the glaze; set both aside separately.
Beat the softened butter and sugar together on medium-high speed for 5–7 minutes until pale, fluffy, and noticeably increased in volume. Scrape down the bowl halfway through.
Add the eggs one at a time, beating on medium speed for 30 seconds after each addition and scraping down the bowl between eggs. The batter should look smooth and glossy after all 6 eggs are incorporated.
Mix in the lemon zest, 3 tablespoons of lemon juice, and vanilla extract on low speed until just combined, about 20–30 seconds.
With the mixer on low, alternate adding the flour mixture in thirds and the sour cream in two additions (flour, sour cream, flour, sour cream, flour), mixing just until combined after each. Finish with a fold using a rubber spatula to ensure nothing is stuck at the bottom.
Pour the batter into the prepared loaf pan, smooth the top, and tap the pan on the counter 2–3 times to release air bubbles. Bake at 325°F for 65–75 minutes, until a skewer inserted in the center comes out clean; tent loosely with foil after 45 minutes if the top is browning too quickly.
In the final 10 minutes of baking, combine 1/2 cup sugar and 1/4 cup lemon juice in a small saucepan over medium heat, stirring until the sugar fully dissolves, about 3–4 minutes. Remove from heat and keep warm.
Remove the cake from the oven and, while still in the pan, poke 20–25 holes over the top with a skewer. Slowly brush all of the warm glaze over the hot cake, letting each application absorb before adding more; allow the cake to rest in the pan on a wire rack for 20–30 minutes.
Lift the cake out of the pan using the parchment sling and cool completely on the rack, at least 1 hour, before slicing. If desired, whisk powdered sugar with 2–3 tablespoons of lemon juice until smooth and drizzle over the fully cooled cake; let set for 15 minutes before serving.