Chop 8 ounces of the white chocolate, read notes on measuring above, and place in a heat safe bowl.
In a small saucepan heat the heavy cream and peppermint extract until it starts to simmer. Remove from heat and allow to cool for a minute, the cream should not be bubbling, then pour it over the chopped chocolate and allow it to sit for about 2-3 minutes.
Stir the chocolate slowly until all the chocolate is melted and it is a nice creamy smooth texture. If there are still bits of unmelted chocolate making the mixture lumpy you can place the mixture in the microwave for 5 second intervals until fully melted. Do not overheat the mixture.
Cover the bowl with the ganache mixture and place in refrigerator to chill. Allow it to chill for at least 2 hours, or until solid. Can be chilled overnight.
Once the ganache is chilled and solid, remove from the refrigerator. Allow to warm for about 5 minutes prior to scooping it out. Using a melon baller, or cookie scoop, or a spoon scoop out the ganache and roll into balls that are about an inch in diameter. Place these onto a cookie sheet that is lined with wax or parchment paper.
Once all the ganache is rolled into balls, place the cookie sheet with the truffles in the fridge to allow to cool for at least 20-30 minutes.
When the truffles are cooled, remove from fridge. Melt the semi-sweet chocolate in a heat safe bowl in the microwave by following the directions, 30 second increments stirring in between.
Dip the truffles one at a time into the melted chocolate using a fork, tap the fork on the side of the bowl to remove excess chocolate. Place the chocolate covered truffles back onto the cookie sheet with wax or parchment paper. Once all truffles are covered, place them back into the fridge for another 20 minutes to allow the chocolate to set.
When the chocolate is set then you can drizzle with any leftover chocolate, or the remaining 4 ounces of white chocolate. While the chocolate is melted dip a spoon into the chocolate and drizzle it over the truffles.
Store the truffles in the refrigerator until ready to serve.