Preheat the oven to 350°F (175°C) and line two baking sheets with parchment paper or silicone mats. Set out the butter, egg, and cream cheese ahead of time so they come to room temperature.
In a large bowl, beat the softened butter with the granulated sugar on medium speed for 2 to 3 minutes, until pale and fluffy, scraping down the sides as needed.
Beat in the egg until fully combined, then add the vanilla extract and mix again until the batter looks smooth and slightly glossy.
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt. Add the dry mixture to the wet ingredients in two additions, mixing on low just until no dry streaks remain.
Use a cookie scoop to portion the dough into balls about 1 ½ tablespoons each, placing them on the lined sheets with at least 2 inches between each one and only 6 cookies per sheet.
Bake for 10 to 12 minutes, until the edges are set and the centers look puffed but still pale. Do not wait for them to brown.
Let the cookies rest on the hot pan for 5 minutes, then transfer to a wire rack and cool fully, about 20 minutes, before adding the topping.
In a clean bowl, beat the cream cheese with the butter until smooth, then add the brown sugar, vanilla, and a pinch of salt. Whip on medium speed for 2 to 3 minutes, until the brown sugar dissolves and the mixture is no longer grainy.
Spread or pipe a generous, fairly flat layer of topping onto each cooled cookie, leaving a small border around the edge so it does not drip when torched.
Sprinkle about 1 teaspoon of granulated sugar evenly over each topping, then hold a torch a few inches above and move it in slow passes until the sugar melts, bubbles, and turns amber. Work in two light passes and let the sugar harden for a minute or two before serving.