Mix the cornstarch and sugar with a hand mixer. Once incorporated, transfer to sauce pan and add cherry juice. Heat until boiling, stirring frequently. Once the sauce thickens, remove from heat and stir in cherries, folding carefully.
Place approximately 1/4 cup of the cherry mixture in each tortilla, roll it in the burrito style. Secure with a toothpick and fry in hot oil until golden brown. Let burritos drain on a paper towel.
To make the glaze, combine milk, powdered sugar and vanilla. Drizzle over hot burritos and let them cool.