Preheat your oven to 350°F (175°C). Grease a loaf pan or line it with parchment paper.

In a saucepan over medium heat, melt the unsalted butter until golden brown, stirring frequently. Remove from heat and let cool slightly.

In a mixing bowl, whisk together the browned butter, granulated sugar, eggs, lemon zest, and milk until smooth.

In another bowl, combine flour, baking powder, and thyme leaves. Gradually fold into the wet mixture until just combined; avoid overmixing.

Pour the batter into the prepared pan and bake for 45-50 minutes or until a toothpick comes out clean.

For the drizzle, mix powdered sugar with lemon juice in a small bowl. Once the cake has cooled slightly but is still warm, pour the drizzle over it.