Preheat the oven to 350°F (177°C) and prepare a 12-count muffin tin with cupcake liners.

In a food processor, pulse the graham crackers until they resemble fine crumbs. Add the brown sugar and melted butter, pulsing a few times until the mixture is combined and resembles damp sand. Spoon about 1 tablespoon of the crust mixture into the base of each cupcake liner. Firmly press down using the bottom of a glass or your fingers to create an even layer. Set aside.

In a medium bowl, sift together the flour, baking powder, baking soda, and fine sea salt. Set this dry mixture aside.

Using a stand mixer or hand mixer, beat the softened butter on medium speed until smooth, about 1 minute. Add in the vegetable oil and granulated sugar, continuing to beat for another 1–2 minutes until light and fluffy.

Scrape down the sides of the bowl as needed. Incorporate the eggs one at a time, ensuring each egg is fully blended before adding the next. Stir in the vanilla extract followed by the room-temperature milk, mixing just until combined.

Gently fold in the dry ingredients with a rubber spatula, being careful not to overmix to preserve the batter’s lightness.

Evenly divide the batter over the prepared graham cracker crusts, filling each liner approximately two-thirds full. Bake in the preheated oven for 18 minutes, but begin checking for doneness at the 15-minute mark. Lightly press the tops of the cupcakes; if they spring back, they are ready. Allow the cupcakes to cool completely before frosting.

In a food processor or blender, grind the freeze-dried strawberries into a fine powder. Sift the powdered strawberries together with the powdered sugar into a large mixing bowl to ensure a smooth consistency.

In the bowl of an electric mixer, beat the softened cream cheese and butter on medium-high speed for about 4 minutes until the mixture becomes airy and pale in color, pausing once or twice to scrape the bowl.

With the mixer off, add the sifted powdered sugar and strawberry powder. Begin mixing on low speed to prevent a dust cloud, then increase to medium-high speed and beat for another minute until fully incorporated.

Add the vanilla extract and cheesecake extract, if using, blending until smooth and well combined.

Transfer the frosting to a piping bag fitted with your preferred tip. Pipe a generous swirl of frosting atop each cooled cupcake.

For a final flourish, top each cupcake with a fresh strawberry if desired. Store the cupcakes covered in the refrigerator for up to 4 days to maintain freshness.