In a medium pot, boil oats and salt in water over high heat. Once mixture comes to a boil, reduce heat to low and add half of the diced apple as well as the pumpkin pie spice. Continue to cook, stirring occasionally, until oatmeal thickens, about 20 minutes.
Remove from heat and stir in remaining apple and walnuts.
Spoon oatmeal into four ramekins and sprinkle brown sugar with a large pinch of kosher salt on top of each serving. Broil under high heat just until all of the sugar melts and bubbles, about 5 minutes.
Serve immediately with a dollop of heavy whipping cream, if desired.