Preheat oven to 375 degrees. Mix flour, baking powder, and sea salt in a large bowl.
Mix milk, butter, sugar, eggs, and vanilla extract in another bowl. Add wet to dry and mix well.
Divide batter evenly into three round, 9-inch pans. Swirl jam through batter.
Bake for about 25 minutes or until a toothpick inserted in the center comes out clean. Meanwhile, beat together frosting ingredients, adding milk last. If desired, swirl some more lingonberry jam into the frosting after it's mixed.
Once cake is baked, cool layers completely then frost.