Combine the cream, sugar, milk, mint, corn syrup, and vanilla bean paste in a medium saucepan over medium-low heat. Bring to a boil. Remove from heat, cover, and let stand 20 to 25 minutes.
Place the cornstarch in a small bowl. Add 3 to 4 tablespoons of the cream mixture and whisk to dissolve the cornstarch. Whisk the cornstarch mixture back into the cream. Bring to a boil over high heat, whisking constantly for 1–2 minutes as the mixture thickens.
Strain the cream through a fine mesh strainer into a bowl set over an ice water bath. When it has chilled to room temperature, refrigerate, covered, at least 4 hours or overnight.
Transfer to an ice cream machine and prepare according to manufacturer’s instructions. Add the chocolate chips as soon the ice cream is finished.
Freeze in a covered containers for 2 to 3 hours or until solid. Ice cream may frozen for up to one month.