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1
Position oven rack in the middle of oven; preheat oven to 300; generously butter and flour a 10-inch Bundt pan.
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2
Bring the milk and thyme just to a boil in a small saucepan over medium heat.
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3
Remove from heat, cover, and steep for 7 minutes; pour through a fine strainer set over a bowl and let the milk cool to room temperature.
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4
In a mixing bowl, whisk the flour, baking powder, and salt together; set aside.
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5
Using an electric mixer on med-high speed, beat the butter in a large bowl until light and fluffy.
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6
Decrease speed to medium and gradually add 1 3/4 cup sugar.
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7
Increase speed to med-high and beat until the mixture is light and fluffy.
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8
Beat in the eggs one at a time, beating well after each addition.
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9
Decrease speed to low and add the flour mixture alternately the milk in 3 batches, beginning and ending with the flour mixture and beating just until blended.
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10
Beat in 2 teaspoons zest and the vanilla; gently stir in berries.
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11
Transfer batter to the prepared pan; smooth the top with a rubber spatula.
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12
Bake for 1 hour and 30 minutes to 40 minutes, or until the cake begins to pull away from the sides of the pan and a pick inserted in the center comes out clean.
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13
Let cake cool in pan on a wire rack for 20 minutes; then turn it out onto the rack and set it right side up.
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14
Meanwhile, bring the remaining 1/2 cup sugar, 2 teaspoons zest, and lime juice to a boil in a small pan over medium heat; remove from heat and let stand for 5 minutes.
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15
Brush the lime juice mixture over the warm cake and let cool completely.
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16
Serve, cut into wedges.
