Prep the oven and pan: Preheat oven to 325°F. Grease a 9×5-inch loaf pan generously and lightly dust with flour if not using parchment. Lining with parchment is ideal for easy removal.
Infuse the sugar: In a small bowl, combine the sugar, lemon zest, finely chopped thyme, and crushed lavender. Using your fingers, rub the mixture for about a minute until it feels slightly damp and fragrant, releasing the natural oils and fully infusing the flavors.
Cream butter and sugar: In a stand mixer, beat the butter with the infused sugar until light and fluffy, about 3 minutes.
Add eggs and vanilla: Beat in the eggs one at a time, mixing well after each addition. Stir in the vanilla.
Mix dry ingredients: In a separate bowl, whisk together flour, baking soda, baking powder, and salt.
Combine wet and dry: Add the dry ingredients to the butter mixture in three parts, alternating with the sour cream. Begin and end with the dry mixture. Mix gently on low speed until just combined - do not overmix.
Pour batter and smooth: Pour the batter into the prepared pan and smooth the top.
Bake the cake: Place the pan on the lower-middle oven rack. Bake for 65–75 minutes, or until a skewer inserted in the center comes out with just a few moist crumbs.
Cool in pan: Allow the cake to cool in the pan for 15 minutes. Then lift it out using the parchment liner (or carefully loosen with a knife if not using parchment) and remove the parchment liner. Place the loaf on a wire rack to cool completely.
Make the glaze: In a small bowl, whisk together the confectioner’s sugar, lemon juice, and milk or cream until smooth and pourable.
Glaze the cake: Using a toothpick, poke a few holes in the top of the cooled loaf to allow the glaze to seep in. Slowly pour or brush the glaze over the top, letting it drip down the sides. Allow the glaze to set for 20–30 minutes.
Slice and serve: Once the glaze has set, slice carefully and enjoy.