Heat oven to 350ºF (177ºC) with rack set in middle position. Coat a 2-quart shallow baking dish with nonstick spray.
In a large nonstick skillet melt 2 tablespoons butter over medium heat. Add 1½ cups oats and sauté until fragrant and toasted, about 4 minutes.
Stir in 1 teaspoon cinnamon, 1 teaspoon ginger, ½ teaspoon cardamom and ½ teaspoon salt; cook until fragrant, about 1 minute. Scrape oats into prepared baking dish; stir in 3 cups milk and 1½ cups warm water.
Bake oatmeal for 1 hour, stirring halfway through. Stir oatmeal, and continue to bake until thick and creamy, about 20 minutes more, stirring every 5 minutes.
Meanwhile, dice remaining 2 tablespoons butter and chill.
Stir oatmeal, then evenly sprinkle diced butter, ⅓ cup pecans and ¼ cup sugar over top. Turn oven to broil and broil until browned, 3–5 minutes.
Serve oatmeal with cream, maple syrup and flaky sea salt, if desired.