Salted Caramel Sheet Cake

Make Cake: Preheat oven to 350 degrees F. Generously grease a 12"-x-17" half sheet/jelly roll pan and sprinkle lightly with flour. Set aside. In a large bowl using a hand-held mixer or stand mixer fitted with a paddle attachment, mix softened butter for about 1 minute on medium speed. Once smooth, add brown sugar and granulated sugar and beat on medium speed until fluffy. Add eggs and vanilla extract and mix until smooth. Add yogurt and mix on medium high speed until combined. In a large bowl, whisk together flour, baking soda, and salt. Pour half of flour mixture into butter mixture and beat on low speed for 5 seconds. Pour in 1/2 cup milk; beat on low speed for 5 seconds. Repeat with remaining flour and milk until combined and smooth. Do not overmix. Spread cake batter into pan and smooth into a thin, even layer with a rubber spatula. Bake until top is lightly browned and a toothpick inserted in the center comes out clean, 20 to 24 minutes. Remove from oven and let cool in the pan on a wire rack. Make the Frosting: Meanwhile, melt butter in a small saucepan over medium heat. Once melted, whisk in brown sugar until completely combined. Bring to a boil, then add 2 tablespoons milk and boil 1 minute more. Remove pan from heat, pour into a large heat-proof bowl, and let cool to room temperature about 45 minutes. Once cooled, add remaining milk, confectioners sugar, vanilla extract, and salt. Using a handheld or stand mixer with a whisk attachment, beat on low speed for 20 seconds, then gradually increase to high speed. Beat on high for 3 minutes. (If frosting is too thick, add 1 tablespoon milk.) Spread frosting on top of cooled cake, then drizzle with caramel sauce and sprinkle with toffee bits and sea salt. Slice and serve. Cover leftovers tightly and store in the refrigerator for up to 5 days.