Whisk cream, milk, and half of the sugar in a medium saucepan over medium heat. Let this heat until bubbles start to form just around the edges and the liquid steams when you stir it.

Meanwhile, whisk egg yolks and remaining sugar in a bowl for 1-2 minutes until light.

Once milk is hot, gradually whisk 1 cup of it into the egg yolks to temper the eggs so they don't scramble.

Pour the tempered egg yolks back into the saucepan with the hot cream mixture and continue to cook, stirring constantly, until thick enough to coat the back of a spoon or the custard reaches 170-175 degrees F on a candy thermometer.

Remove the ice cream base from the heat and stir in the peppermint extract, vanilla extract, and food coloring, if using. Place the pan into an ice bath to cool the mixture down quickly, then chill thoroughly before churning.

To churn the ice cream, transfer the mint base the frozen bowl of an ice cream maker. It will need to churn for 20-30 minutes to be the consistency of soft serve.

While the ice cream is churning, melt the chopped chocolate and coconut oil in a medium bowl by heating in the microwave in 20 second increments. Stir well between each burst of heat until the chocolate is melted and smooth (about 60-90 seconds total). Let this cool until just warm.

When the ice cream is almost done, start drizzling the chocolate in while the ice cream is churning. The chocolate will freeze on impact and shatter into small pieces and chunks. I like to hold some of the melted chocolate in reserve for layering with the ice cream, but you can add it all this way if you prefer.

Transfer half of the ice cream, which should be soft serve consistency, to a freezer safe container. Drizzle any reserved melted chocolate over the top, then add the remaining ice cream. Freeze for 4-6 hours to harden and cure so it is scoopable. Let the ice cream sit out for 10-15 minutes before scooping for best results.