In a small bowl, toss the apple slices with the lemon zest, lemon juice, sugar, cinnamon, and salt, and set aside.
In another small bowl, mix the flour, brown sugar, oats, and salt with a fork until uniform. In a baking dish, melt the butter in the microwave until about half melts, 10 to 15 seconds on high.
Pour the butter into the flour mixture and incorporate with a fork. Leaving the excess butter in the baking dish, arrange the apple slices in the dish. Top with the flour-oat mixture.
Bake until the apples are cooked through and the topping is golden, about 45 minutes.
In a medium-heavy saucepan, mix the water and sugar and bring to a boil over medium-high heat. Allow the mixture to boil, without stirring. Cook's Note: Swirl the pan, if needed. Boil until the sugar mixture is pale golden brown, approximately 7 minutes. Cook's Note: Watch closely; sugar burns quickly.
Remove the pan from the heat, and stirring vigorously add the butter and cream. The mixture will bubble.
Add the cardamom seeds and stir to incorporate. Return the pan to the heat and bring the mixture to a boil and then remove from the heat and allow to cool a few minutes. Stir in the vanilla extract and strain the sauce before drizzling over the cobbler.
