My favorite way to use fresh mint is to make mojitos, a Cuban rum drink. You first need to make a simple syrup using 1 part sugar and 1 part water. Combine the sugar and water in a small saucepan, bring to a boil, and stir until all the sugar is dissolved. Cool. Next, place a couple of lime wedges and mint sprigs in a cocktail shaker and muddle well. Then add 1 tablespoon of the simple syrup, 1 ounce of white rum, and a splash of club soda. Shake to blend and pour into a glass over ice. Garnish with mint leaves. This makes a great summer drink!
I think your orange mint plant would work great for this recipe.