Heat sugar and water in a small saucepan over medium heat to melt the sugar. Continue cooking and swirling sugar until it turns amber in color.
Whisk in sea salt and heavy cream. The mixture will bubble up violently briefly. Continue whisking until sauce is smooth.
Stir in butter and vanilla. Set aside.
For the Crumble
Combine all ingredients together using a stand mixer. The mixture will be crumbly but stay together when squeezed. Set aside.
For the Apples
Prepare apples and toss in lemon juice.
Cook apples in a large cast-iron skillet over medium-low heat in butter to draw out moisture. Sprinkle with salt to draw out all the moisture possible. Drain apples and place back into skillet. This process should take about 5-7 minutes of cooking.
Pour 3/4 of prepared caramel sauce into the apples and stir gently.
Top with the crumble topping.
Bake at 350 for 20 minutes and serve with remaining caramel sauce.