Crust Preparation

1. Preheat the oven to 325°F (165°C).
2. Crush graham crackers into fine crumbs.
3. In a bowl, mix the crumbs with sugar and melted butter until it resembles wet sand.
4. Press the mixture firmly into the bottom and slightly up the sides of a 9-inch springform pan.
5. Pre-bake the crust for 8 to 10 minutes.

Filling Preparation

1. In a mixing bowl, beat softened cream cheese and sugar until smooth.
2. Add sour cream and vanilla extract, and mix until combined.
3. Add eggs one at a time, mixing on low speed until just incorporated.

Strawberry Swirl Preparation

1. Cook strawberries with sugar and lemon juice over medium heat until juicy.
2. Mash the strawberries and simmer for 5 to 8 minutes until slightly thickened.
3. If desired, mix cornstarch with water and stir in the strawberry mixture to thicken it further.
4. Cool the strawberry puree before swirling.

Assembling and Baking

1. Pour cheesecake filling into the pre-baked crust.
2. Spoon dollops of cooled strawberry puree on top of the batter.
3. Use a knife to swirl the strawberry puree gently into the cheesecake batter.
4. Bake at 325°F (165°C) in a water bath, if desired, for 55 to 75 minutes.

Cooling and Setting

1. Turn off the oven and let the cheesecake cool in the oven for 1 hour with the door cracked.
2. Move to room temperature, then chill for at least 6 hours or overnight.