Combine milk, sugar, cocoa and cornstarch in a pan. Bring to a boil over medium-high heat, whisking. Cook until mixture thickens, about 1 minute. Remove from heat. Whisk in chocolate until melted. Fill a large bowl with ice. Place pan in ice; let cool, stirring, until mixture is cold, about 20 minutes.
Transfer mixture to a blender. Add avocado flesh, vanilla and salt; process until smooth. Divide mixture among 10 (1/2-cup) pop molds. Insert pop sticks and freeze until firm, about 3 hours.