Preheat the oven to 350°F (180°C) and line the muffin pan with 12 cupcake liners. Set aside.
To unsweetened almond milk, add apple cider vinegar. Mix and set aside.
In a medium-size bowl, using a whisk, combine all-purpose flour, cornstarch, baking powder, baking soda, and a pinch of sea salt.
To a large bowl, add granulated sugar, sunflower oil, vegan yogurt, and vanilla extract, and whisk to combine. Add almond milk mixture and mix until incorporated. Sift in dry ingredients and mix until just combined.
Divide the batter evenly into 12 cupcake liners. Bake in preheated oven for 20 minutes or until a toothpick inserted into the middle comes out clean. If it looks wet, bake for about 5 minutes longer. Transfer to a cooling rack and allow to cool completely before frosting.
Add soft vegan butter and cream cheese to a large bowl (alternatively, add them to a stand mixer with the whisk attachment) and cream with a hand mixer on high speed until fluffy and lighter in color for about 2-3 minutes. Add in powdered sugar and mix until fully combined. While mixing, add one tablespoon at a time of almond milk and mix until incorporated and fluffy.
Divide the frosting equally between 5 bowls. Tint each with natural dye – whisk in ¼ tsp ground turmeric for yellow, ¾ tsp matcha powder for green, 1/8 tsp blue spirulina powder for blue, 4 tsp freeze-dried raspberry powder for pink, and 1/8 tsp blue spirulina powder + 3 tsp freeze-dried raspberry powder (or 4 tsp freeze-dried blueberry powder) for purple color.
Using a large piece of food plastic wrap, spread each color in a line along the width of the wrap. Carefully wrap the frosting into a large log. Overlap plastic wrap and twist ends to seal.
Prepare a piping bag with a star tip. Cut off one end of the frosting warp, and insert the wrap into the prepared piping bag. Pipe rainbow swirls on each cupcake as desired.
Serve immediately or store them in the fridge in an airtight container.