In a large bowl, beat the cream cheese with an electric mixer until light and fluffy, about 1 ½ - 2 minutes. Add the dry pudding mix and about ¼ cup of the milk. Mix until well combined. It will be very thick, which is fine! Gradually add the remaining milk, mixing constantly, until the mixture is completely combined (a few lumps are fine). Dollop the jam into the by the tablespoonful, and then use a knife to gently swirl the jam into the pudding mixture. Streaks of jam are good – it doesn’t need to be completely combined. Gently fold in half of the Cool Whip, being careful not to stir too vigorously, which will deflate the light, airy texture.
Spread about ¼ cup of the pudding mixture in a very thin layer in the bottom of a deep 8-inch or 9-inch square dish. Add a layer of graham crackers on top, breaking the crackers as needed to fit.
Spread ⅓ of the remaining pudding mixture on top of the graham crackers. Top with about ⅓ of the strawberries. Repeat the layers twice more to use up the remaining graham crackers, pudding, and strawberries.
Spread the remaining half of the Cool Whip on top.
Cover and refrigerate for at least 4 hours or overnight. If desired, garnish with additional sliced strawberries just before serving.