Rinse out the saucepan or wipe it clean. Add the remaining 1 can (14 oz) of sweetened condensed milk and heat over low, just until warm and pourable. Remove from the heat and stir in the peppermint extract until fully combined.
Add the remaining 1 cup of semisweet chocolate chips to the warm mint mixture and stir gently. The chocolate will melt in streaks, turning the mixture a soft greenish-brown with visible swirls of chocolate. Keep stirring until it is mostly combined but still marbled—this gives you that pretty green and brown effect in the finished fudge.
Carefully pour the mint mixture over the cooled chocolate layer in the pan. Use a spatula to spread it evenly, then lightly drag the spatula or the tip of a butter knife through the top in a few gentle swirls to enhance the marbled green-and-brown look.
Refrigerate the fudge, uncovered, for at least 2 to 3 hours, or until firm enough to cut. For the cleanest slices, let the pan sit on the counter for about 10 minutes before cutting so the fudge isn’t rock hard.