Preheat your oven to 350°F (175°C). In a mixing bowl, combine all-purpose flour, old-fashioned oats, and brown sugar. Cut in cold butter until the mixture resembles coarse crumbs. Press this mixture into the bottom of a greased 9x9-inch baking pan. Bake for 15-20 minutes, or until lightly golden and fragrant.

In a large mixing bowl, beat the cream cheese with an electric mixer on medium speed until smooth and creamy, about 2-3 minutes. Gradually add in sugar, salt, ground cinnamon, nutmeg, and vanilla extract, mixing well to ensure no lumps remain. Incorporate one room temperature egg until fully combined and velvety.

Gently fold the diced rhubarb into the cheesecake filling using a spatula, ensuring even distribution without breaking it down.

Pour the rhubarb cheesecake filling over the pre-baked crust, smoothing the top. Bake for 25-30 minutes; the edges should be set and lightly browned, and the center may jiggle.

Allow the squares to cool in the pan for at least 1 hour at room temperature. Transfer to the refrigerator to chill for 2 hours. Cut into squares and serve chilled or at room temperature.