Arrange a rack in the middle of the oven and heat to 325°F. Line a 12-cup standard muffin tin with paper liners.

Place the graham cracker pieces in the bowl of a food processor fitted with the blade attachment. Process into fine crumbs, about 30 seconds. Slowly add the butter and pulse to combine into moist crumbs. (If using graham cracker crumbs, just mix with the butter in a bowl.) Divide the mixture evenly among the muffin wells (a scant tablespoon per well) and press with your fingers to form a firm, even layer on the bottoms.

Place the cream cheese in the bowl of a stand mixer fitted with the paddle attachment. (Alternatively, use an electric hand mixer and large bowl.) Beat on medium speed until very smooth, about 2 minutes. Gradually beat in the sugar and salt until incorporated, about 1 minute more. Stop the mixer and scrape down the sides of the bowl.

With the mixer on medium speed, beat in the eggs 1 at a time, waiting until the first egg is fully incorporated before adding the second. Add the vanilla and beat until just combined. Divide the mixture evenly among the muffin cups (about ⅓ cup each).

Bake until the edges are set but the center still jiggles slightly, 20 to 25 minutes. Place the muffin tin on a wire rack and cool completely, about 1 hour. Cover with aluminum foil and refrigerate until completely chilled, at least 2 hours or overnight.

Uncover the muffin tin and carefully remove the mini cheesecakes. Top each with 3 raspberries and dust with powdered sugar before serving.