Let your cream cheese set on the counter for a few hours until it is soft. Cut a round piece of parchment paper or foil to line the bottom of a 9" springform pan.
Wash, hull, and dice the 2 cups of berries. Place them in a heavy saucepan with the 3 tablespoons of sugar. Cook them over medium heat until softened, then mash with a potato masher.
Continue cooking and stirring the berry mixture until thickened and reduced down to about 2/3 cup. Place the pan in a bowl or pan of ice water to cool down quickly.
Finely crush the graham crackers in a food processor or blender. Stir together the crumbs, 1/4 cup sugar, and melted butter in a small bowl. Press the mixture firmly into the bottom of the lined springform pan; set in the fridge or freezer to chill.
Beat the cream in the chilled bowl until stiff peaks form; place in the fridge.
In a large mixing bowl, beat the cream cheese until very smooth and creamy. Add the powdered sugar, lemon juice, vanilla, and salt. Blend until smooth, occasionally scraping the sides of the bowl with a silicone spatula. Fold in the chilled strawberry puree.
Pour the filling into the crust and level it out with an offset spatula or large spoon.
Cover the pan with foil or plastic wrap. Chill for at least 4-6 hours, but overnight is better.
When ready to serve, remove the sides of the springform. Transfer the cheesecake to a serving plate. (Parchment makes it MUCH easier.)
For topping, beat the cream until soft peaks form. Add the powdered sugar and vanilla, beat again until stiff peaks form.
Slice cheesecake and garnish each slice with whipped cream and a fresh strawberry.