Pudding Recipe Adjustment HELP (Dairy Free, Recipe Included)

I'm no newb in the kitchen, but I'm a newb with cornstarch ::blush::. I know, I know, how do I make gravies and roux? I use flour and I avoid recipes that call for cornstarch.

However, there are several lactose-free and dairy-free and vegan recipes that don't rely on animal milk or gelatin (an animal by-product) that require it that my lactose-intolerant daughter is asking for.

One thing she's been begging me to make is a vanilla version of her chocolate soymilk pudding. I do follow that recipe pretty closely since I only recently started making it, but I'm not confident enough with cornstarch yet to adjust the recipe. It calls for regular soymilk plus the cornstarch plus cocoa powder. I need to eliminate the cocoa powder. [edited: I use Very Vanilla flavor of soymilk]

How do I adjust the recipe? Do I reduce the soymilk? Or increase the cornstarch? Something I'm not thinking of?

Dairy Free Chocolate Pudding
Allrecipes.com
adjusted for 4 servings
1/4 cup and 2 tablespoons cornstarch
1/4 cup water
3 cups soy milk
1/2 teaspoon vanilla extract
1/2 cup white sugar
1/2 cup unsweetened cocoa powder

In small bowl, combine cornstarch and water to form a paste.

In large saucepan over medium heat, stir together soy milk, vanilla, sugar, cocoa and cornstarch mixture. Cook, stirring constantly, until mixture boils. Continue to cook and stir until mixture thickens. Remove from heat. Pudding will continue to thicken as it cools. Allow to cool five minutes, then chill in refrigerator until completely cool.

*Notes: combine dry ingredients first, then whisk into wet ingredients.