Preheat the oven to 350ºF (180ºC). Line 2 large cookie sheets with parchment paper.
In a medium-sized bowl, whisk together the flour, cornstarch, baking soda and salt until well blended.
In a large bowl, beat the butter until smooth, with an electric mixer at medium speed. Add the peanut butter and beat until smooth and combined.
Place 2 tablespoons (25g) of granulated sugar in a small shallow bowl and set it aside. Add the remaining granulated sugar and the brown sugar to the butter and peanut butter mixture. Beat on medium speed until pale and fluffy. Beat in the maple syrup, egg and vanilla extract in 3 separate additions, making sure each one is incorporated before adding the next addition. On low speed, or by hand, stir in the flour mixture just until combined.
Roll the cookie dough into balls, about 2 3/4-tablespoons (50g) each. (I used a # 24 portion scoop.*) Roll balls into the reserved sugar, coating them all over. Place the dough balls onto the prepared cookie sheets about 3 inches apart.
Bake the cookies until the centers are slightly puffed and the edges are starting to turn golden brown, about 11-13 minutes. Let the cookies cool on the baking sheet for 4-5 minutes, then transfer them to a cooling rack. The cookies will be fragile at first but will firm up as they cool.