Make dry-method caramel: Melt 1 cup sugar in dry saucepan over medium heat, stirring occasionally until deep amber. Remove from heat, whisk in 6 Tbsp butter, then slowly add 1/2 cup cream and 1 tsp salt. Cool completely.
Preheat oven to 325°F. Grease springform pan. Combine 2 cups graham crumbs, 3 Tbsp sugar, and 1/2 cup melted butter. Press firmly into bottom and 1 inch up sides. Bake 10-12 minutes, then cool and reduce oven to 300°F.
Beat 32 oz softened cream cheese on low speed until smooth. Add 1 cup sugar and mix until incorporated. Add 1/4 cup sour cream and 2 tsp vanilla, then add eggs one at a time on low speed.
Gently fold 1/2 cup cooled salted caramel sauce into the batter until just swirled. Tap bowl to release air bubbles.
Wrap springform pan in two layers of foil and place in roasting pan. Pour batter over crust. Place pan in oven and carefully add hot water to roasting pan until 1 inch up the sides.
Bake at 300°F for 55-70 minutes until edges are set and center has a gentle jiggle. Turn off oven, prop door open, and leave cheesecake inside for 1 hour.
Remove from water bath, run a knife around edges to loosen, and cool completely on wire rack for 1-2 hours. Cover and refrigerate at least 6 hours or overnight.
Warm remaining caramel sauce until pourable. Release springform pan, drizzle caramel over top, and sprinkle with 1/2 tsp flaky sea salt. Slice with a hot, dry knife.