Preheat oven to 350°F (175°C). Grease a 9x5-inch loaf pan and line it with parchment paper.
Mix dry ingredients: In a medium bowl, whisk together flour, baking powder, baking soda, salt, and culinary lavender.
Combine wet ingredients: In another bowl, mix melted butter, coconut milk, sugar, eggs, and vanilla extract until smooth.
Fold dry into wet: Gently mix the dry ingredients into the wet mixture until just combined. Do not overmix. Batter should be slightly lumpy.
Pour and bake: Pour batter into prepared pan. Bake 45–55 minutes, or until a toothpick inserted in the center comes out clean.
Cool slightly and glaze: Let the cake cool for 10–15 minutes. Mix powdered sugar with coconut milk to make a thin glaze and drizzle over the top.
Serve and enjoy: Slice and enjoy warm or at room temperature.