Cut parchment paper into 2 inches by 2 inches squares and set aside.
Add butter into a large bowl and beat until creamy. Add powdered sugar to the creamed butter and beat again until it is creamy and fluffy. Add vanilla extract and beat again until well combined.
Scrape the bottom and sides of the bowl at least once half way through to make sure the butter and sugar are well combined.
If the icing is too stiff, add some milk. Do it is small increments of half a teaspoon to make sure the buttercream does not become too soft (see Note 1).
Remove some of the icing into a small bowl and tint it white for the flower centers.
Divide the remaining into 2 medium bowls. Tint the first bowl with navy blue and add a tiny bit of royal blue and a small tinge of black to it. Mix well.
Tint the second bowl with turquoise food coloring. Mix well.
Transfer the white frosting into a piping bag fitted with round tip #3. Transfer the blue and turquoise frosting into 2 separate piping bags (without any tips attached). In a separate piping bag, fit the petal tip #104 (see Note 2).
Snip the tip of the piping bag with navy blue buttercream. Insert the bag into the piping bag fitted with petal tip #101.
Dab a little icing onto the flower nail. You can use the blue or turquoise icing.
Stick a parchment square onto the flower nail. The buttercream acts to hold the paper in place while you are piping the flower.
Hold the flower nail in your left hand and the piping bag on your right with the tip positioned at a 45 degrees angle from the paper. Make sure the narrow end of the tip is on the top and the wider end at the bottom (see Note 3).
To pipe the petals, place the bottom of the tip in the center of the flower nail. Simply rotate the top of the tip (while gently squeezing the piping bag) in a circular motion until you get the shape of a petal. Lift the tip.
Repeat the step and pipe the second petal, followed by the third, forth and fifth. In piping the petals, always rotate the flower nail such that the petal you will be piping next is always at an angle that is comfortable for you. As you finish piping each petal, rotate the flower nail.
Gently slide the paper away (pull it sideways) from the flower nail and place it on a flat cake board. Once all cake board is filled, place it in the freezer for approximately 30 minutes until the buttercream flowers have hardened. Keep them in the freezer until ready to use.
To place the flowers on a cake or cupcake, remove them from the freezer (see Note 4). Peel half of parchment paper underneath each flower and use a spatula to lift the flower off the paper. Position the flower on your cake or cupcakes as you wish.
Use the white icing fitted with round tip #3 to pipe tiny white dots for each flower center to complete them (see Note 5).