Mix ¾ cup all-purpose flour, ¼ cup packed light brown sugar, 1 teaspoon pumpkin pie spice, and ¾ teaspoon kosher salt together in a 14-ounce or larger microwave-safe mug or deep ramekin with a whisk or fork. Remove ¼ cup of the flour mixture and set aside.

Microwave 4 tablespoons unsalted butter in a small microwave-safe bowl on HIGH power until melted. Stir in 3 tablespoons of the melted butter, ¼ cup pumpkin purée, ¼ cup whole milk, and ½ teaspoon baking powder to the mug with a fork until a smooth, loose batter forms with no pockets of unincorporated flour.

Add the reserved flour mixture to the bowl with the remaining 1 tablespoon melted butter and stir with a fork until moistened and crumbly. Scatter the streusel over the cake batter.

Microwave the mug cake on HIGH power until a tester inserted into the center comes out mostly clean with just a few moist crumbs stuck to it, about 1 minute and 45 seconds. Cooking time will vary greatly depending on the strength of your microwave. Start with 1 ½ minutes and check for doneness before adding more time.

Meanwhile, if making the drizzle, stir 2 tablespoons powdered sugar and ¾ teaspoon whole milk together in a clean, small bowl with a fork until smooth. Add more milk to thin it out as needed so that it is pourable. Drizzle over the mug cake and let cool for 3 to 5 minutes before serving.