Whisk together the flour, baking powder, and salt in a medium bowl; set aside.
In a large bowl, beat the softened butter, brown sugar, and lemon zest with a hand mixer on medium-high until light and fluffy, about 2 minutes. Scrape the bowl.
Beat in the egg and vanilla until smooth and slightly thickened, 30–45 seconds.
Switch to low speed and mix in the dry ingredients just until no dry streaks remain. Cover and chill the dough for 20 minutes to firm up for cleaner shaping.
Preheat the oven to 340°F (170°C). Line two baking sheets with parchment paper. If you like, briefly toast the graham crumbs in a dry skillet over medium-low heat for 1–2 minutes, stirring, then cool completely for extra aroma.
Scoop the dough into 16 portions (about 1½ tablespoons each) and roll into balls. Arrange 2 inches apart on the prepared sheets. Using a lightly floured teaspoon or your thumb, press a deep well in the center of each ball before baking.
Bake 13–15 minutes, rotating the pans halfway, until the edges are set and just turning golden while the centers remain pale. If any wells puff, re-press gently with the back of a spoon right after baking. Cool cookies completely on the sheets.
Make the filling: beat the cream cheese and powdered sugar on medium until silky and lump-free, 1–2 minutes. Mix in the vanilla just to combine. Transfer to a piping bag or a zip-top bag with a corner snipped.
Pipe or spoon the cheesecake filling into the cooled cookie wells. Sprinkle each cookie with graham crumbs, gently pressing so they adhere. Serve at room temperature or lightly chilled.