Heat the oven to 350°F. Have an ungreased 9 x 9-inch pan ready before mixing so the crumb mixture stays cool.
Stir the flour, old-fashioned oats, brown sugar, and Morton kosher salt together in a medium bowl. Mix until the brown sugar is evenly dispersed and no salty pockets remain.
Cut the softened, unmelted butter into the dry ingredients with a rigid pastry blender. Stop when the mixture forms rough, pea-sized crumbs with no large streaks of butter.
Press half of the crumb mixture firmly across the bottom of the pan and reserve the rest. The base should look level and compact, with the remaining crumbs still loose for sprinkling.
Beat the softened cream cheese, granulated sugar, and egg in a stand mixer for about 1 minute. The filling should look very smooth and creamy, without visible cream cheese lumps.
Mix in the vanilla extract, cinnamon, and nutmeg just until they disappear into the filling. Stop once the spices are evenly blended so the egg is not overworked into a dense filling.
Fold in the chopped rhubarb with a spatula. Use a light hand to keep the fruit pieces intact and avoid streaking the filling pink.
Spread the rhubarb filling over the crust, then scatter the reserved crumbs evenly over the surface. Cover the filling from edge to edge without pressing the topping down.
Bake for 40 minutes. The crumble should be lightly browned, and the center may have a slight wobble before it cools and firms.