Preheat oven to 350°F (175°C). Line a 9x13-inch pan with parchment or foil, leaving an overhang.
Mix flour, brown sugar, oats, cinnamon, and salt. Stir in melted butter until crumbly. Press two-thirds into the pan to form crust; set aside the rest.
Combine rhubarb, sugar, cornstarch, and lemon juice in a saucepan. Cook over medium heat, stirring until thickened (7–10 minutes). Cool slightly.
Beat cream cheese and sugar until smooth. Add eggs one at a time, then vanilla, mixing well.
Spread cheesecake over crust. Spoon rhubarb on top, then sprinkle remaining crumble.
Bake 40–45 minutes until golden and center jiggles slightly. Cool completely, then refrigerate at least 2 hours before slicing.