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1
Heat the oven to 375u00b0 F. Add the butter and mint to a small saucepan over medium heat. Once the butter is melted, continue to cook for 2 to 3 minutes, until the mint is very fragrant. Set aside for 30 minutes.
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2
While the butter infuses, hull and halve the strawberries. Lay them in a 9- by 13-inch baking dish (or other large casserole) and toss with the sugar, salt, and ginger. Add the fresh mint. Roast for 45 minutes, stirring once or twice, until the strawberries are soft and very syrupy.
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3
While the berries roast, finish the cookie dough. Use a fine mesh sieve to strain the butter into the bowl of a stand mixer. Press the mint with a spatula or the back of a spoon to release all of that butter! Add the sugars and mix on medium-low speed until creamy and fluffy, 3 to 5 minutes.
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4
Add the egg and vanilla and mix until completely combined. In a small bowl, whisk together the flour, baking soda, salt, and crystallized ginger, if using. Add to the bowl of the stand mixer and mix on low until just combined. Stir in the chopped white chocolate, then scoop onto a sheet of plastic wrap, flatten into a disc, and chill for 1 hour.
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5
While you wait, tend to the strawberries. When they're finished, take them out and allow them to cool slightly. Remove the mint sprigs.
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6
When the dough is chilled, distribute the other berries over the roasted strawberries. Now rip off small chunks of your chilled dough (the size of a couple tablespoons) and scatter over the berries. Send back into the oven for 15 to 20 minutes, until the cookie top has set. Let cool for 5 to 10 minutes, then devour.
