Preheat oven to 350°F and line a 9x13-inch pan with parchment paper, leaving overhang for easy lifting. The oven should be fully preheated before baking the crust.

Mix all-purpose flour, old-fashioned oats, brown sugar, and melted butter until the mixture looks evenly moistened and clumps when pressed. Press firmly into the lined pan to create an even layer.

Bake the crust at 350°F for 15 minutes until lightly golden around the edges. You should see the top set and smell nutty as it bakes.

Beat cream cheese and sugar until smooth and glossy, scraping the bowl as needed to remove lumps. Stop mixing only when no streaks remain.

Add eggs one at a time, mixing just until each is incorporated, then mix in vanilla extract. The batter should look smooth and pourable with a uniform color.

Pour the cheesecake mixture over the hot crust and spread gently to level the surface. Stop once the layer is even, without pressing down.

Simmer diced fresh rhubarb, sugar, and water over medium heat until the rhubarb turns tender and releases juice, about 8-12 minutes. Look for softened pieces and a bubbling, syrupy texture.

Stir cornstarch mixed with a little water into the rhubarb and cook until thick, 1-2 minutes. The swirl should coat a spoon and look glossy rather than watery.

Drop spoonfuls of the rhubarb mixture over the cheesecake and swirl with a knife in gentle figure-eights. The swirls should remain visible as ribbons on top.

Bake at 350°F for 35-40 minutes until the center is set with a slight jiggle. You should see the edges puff and the top look set, not wet.

Cool the bars completely at room temperature, then refrigerate for 4 hours before cutting. Chilled bars slice cleanly and keep the swirl pattern intact.