Prep Pan & Oven – Pre-heat oven to 350 °F / 175 °C. Grease a 9-inch springform pan; line base with parchment.

Red Velvet Batter – Whisk flour, cocoa, baking soda, and salt. In a second bowl beat sugar, egg, buttermilk, oil, vinegar, vanilla, and red coloring. Fold dry mix into wet just until combined; pour into pan.

Bake Cake Layer – Bake 18–20 min until a toothpick shows a few moist crumbs. Cool on a rack. Reduce oven to 325 °F / 165 °C.

Cheesecake Batter – Beat cream cheese until silky. Mix in sugar and sour cream. Add eggs one at a time, scraping bowl, then vanilla.

Water-Bath Bake – Wrap pan exterior in double foil. Pour cheesecake batter over cooled red-velvet base. Set pan in a larger roasting pan, add 1 inch (2.5 cm) hot water. Bake 55–65 min until edges are set and center jiggles slightly.

Gradual Cool – Turn off oven, crack door, and let cake cool inside 1 h. Remove water bath; cool to room temp, then chill ≥ 4 h (or overnight).

Strawberry Topping – Toss berries with sugar and lemon juice. In a small saucepan simmer half the berries with 2 Tbsp water 3 min until softened. Stir in cornstarch slurry (if using) and cook 1 min until glossy. Cool, then fold in remaining fresh slices.

Finish & Serve – Spoon chilled strawberries over cheesecake. Release springform ring, slice with a hot, wiped knife, and serve.