Step 1

FOR THE JAM FILLING: Process sugar, pectin, and salt in food processor until combined, about 3 seconds. Add blueberries and pulse until coarsely chopped, 6 to 8 pulses. Transfer blueberry mixture to medium saucepan and bring to simmer over medium heat, stirring occasionally, until mixture is bubbling and just starting to thicken, 6 to 8 minutes. Off heat, stir in lemon juice. Transfer 1⅓ cups jam to small bowl, cover, and refrigerate until firm, about 3 hours. Strain remaining jam through fine-mesh strainer, cover, and set aside. (You should have at least ¼ cup.)

Step 2

FOR THE FROSTING: Using stand mixer fitted with paddle, beat butter and sugar on medium-high speed until light and fluffy, about 3 minutes. Add cream cheese, 1 piece at a time, and beat until no lumps remain. Add vanilla and 2 tablespoons strained jam and mix until incorporated. Transfer ⅓ cup frosting to each of 2 small bowls. Add 1 teaspoon strained jam to first bowl and 1 tablespoon strained jam to second bowl, stirring well to combine. (You should have 3 shades of frosting.)

Step 3

Place 1 cake round on cake turntable. Spread ⅔ cup chilled jam in even layer over top. Place second cake round on top of jam and repeat with remaining chilled jam. Place third cake round on top. Spread small amount of lightest-colored frosting in even layer over top and sides of cake. Using small offset spatula, spread darkest-colored frosting over bottom third of sides of cake, medium-colored frosting over middle third, and remaining lightest-colored frosting over top third. While spinning cake turntable, run spatula from bottom to top of side of cake to blend frosting colors. While spinning cake turntable, run spatula over top of cake, working from outside in to create spiral. Serve.