The thyme works a little magic by enhancing the flavor of the blueberries. Don't use large highbush blueberries for this cake, if possible; you'll be much happier with the small wild berries. You might instead use the tiny, intensely flavored dried blueberries - a generous cup would be perfect.

Step 1: Position a rack in the middle of the oven and preheat the oven to 300°F. Generously butter and flour a 10-inch (12-cup) Bundt pan.

Step 2: Bring the milk and thyme just to a boil in a small saucepan over medium heat. Remove from the heat, cover, and steep for 7 minutes, then pour through a fine strainer set over a bowl and let the milk cool to room temperature.

Step 3: Whisk together the flour, baking powder, and salt in a medium bowl.

Step 4: Beat the butter with an electric mixer on medium-high speed in a large bowl until light and fluffy. Reduce the speed to medium and gradually add 1/4 cups of the sugar. Increase the speed to medium-high and beat until the mixture is light and fluffy. Beat in the eggs one at a time, beating well after each addition. Reduce the speed to low and add the flour mixture alternately with the milk in 3 batches, beginning and ending with the flour mixture and beating just until blended. Beat in 2 teaspoons of the zest and the vanilla. Gently stir in the berries. Transfer the batter to the pan and smooth the top with a rubber spatula.

Step 5: Bake for 1 hour and 30 to 40 minutes, or until the cake begins to pull away from the sides of the pan and a wooden pick inserted in the center comes out clean. Let the cake cool in the pan on a wire rack for 20 minutes, then turn it out onto the rack and set it right side up.

Step 6: Meanwhile, bring the remaining 1/2 cup sugar, 2 teaspoons zest, and the lime juice to a boil in a small saucepan over medium heat. Remove from the heat and let stand for 5 minutes.

Step 7: Brush the lime juice mixture over the warm cake and let cool completely. Serve, cut into wedges.