Line muffin pan:

Place paper liners in a 12-cup muffin pan.

Prepare colored batters:

For the muffin batter: Cream 1 1/4 sticks (150 g) softened butter, 1 cup (200 g) sugar, and 1 packet vanilla sugar until fluffy. Beat in 3 eggs one by one, mixing thoroughly after each addition. In a separate bowl, whisk 2 1/2 cups (300 g) flour, 1 tsp baking powder, and 1/4 tsp salt. Add the flour mixture and 1/2 cup (125 ml) milk alternately to the butter mixture, stirring until just incorporated. Portion the batter equally into 6 small bowls. Color each portion with 4-5 drops of a distinct food coloring (red, orange, yellow, green, blue, violet).

Layer batters in cups:

Using a teaspoon, spoon the colored batters into each liner in layers: start with orange, then red, violet, and finish with blue, green, and yellow.

Bake muffins:

Bake at 350°F (175°C) in a preheated oven for about 25 minutes. Take out, let cool in the pan for a few minutes, then move to a wire rack to cool entirely.

Make cream cheese frosting:

For the frosting: Using an electric mixer on high, beat 3 1/2 tbsp (50 g) softened butter for 2-3 minutes until pale and creamy. Add 1/3 cup (50 g) powdered sugar and beat another 2-3 minutes until lighter. Mix in 1 tsp vanilla extract. Gently fold in 1/2 cup (100 g) softened cream cheese, a spoonful at a time, until smooth and creamy.

Pipe frosting and add rainbows:

Place the frosting in a piping bag with a 16 mm round tip and refrigerate for 30 minutes. Pipe 6 dollops of frosting onto each muffin. Cut the rainbow gummy strips in half and insert one half into the frosting on each muffin, ends downward, so they stand upright like a rainbow.