In a mixing bowl, beat or vigorously whisk together the sugar and eggs.
Gradually whisk milk into egg mixture, then add back to saucepan and stir with a wooden spoon until slightly thickened. Tracks should form on the spoon. Also, this shouldn't take long -- maybe 5 minutes.
Remove from heat and whisk in the ricotta cheese, letting it melt into the custard.
Strain into a clean bowl. Whisk in the heavy cream, vanilla and lemon.
Cover loosely with plastic wrap and chill for a few hours or overnight until very cold.
Following the ice cream machine directions, churn your ice cream.
Meanwhile, melt the chocolate and coconut oil together in a microwave. Let cool slightly. Remove your ice cream container from the machine and drizzle the chocolate mixture right into it. If it doesn't set immediately, put the whole canister in the freezer for a minute to set the chocolate.
With a big spoon, break up the chocolate pieces and stir into the soft ice cream. Spoon into containers.
Notes
Cook time is really chill time. Make sure you use peppermint extract rather than mint extract since mint extract is usually spearmint. For the chocolate chunks, you need to melt the chocolate, spread it on a parchment or foil lined plate, then re-freeze and chop. For softer chocolate you can mix in a tiny bit of refined coconut oil, but just the process of melting and refreezing will change the chocolate so that it melts in your mouth.For fresh mint ice cream, start by putting 1 cup milk and 1 cup of the cream in a large saucepan along with about 20 mint leaves. Bring to a simmer, then turn off heat and let steep for 10 minutes. Push through a sieve, then follow recipe as directed using the mint flavored milk/cream mixture.