Hi,
This isn't a Bavarian cream recipe because I don't know how to make Bavarian cream without using heavy cream, but this may work for you since it is vegan. Its been eons since I've made it, so I don't remember what it tastes like.
Make Cream Filling:
1/4 cup nonhydrogenated shortening
1/4 cup nonhydrogenated margarine
1 cup powdered sugar
1 tsp. vanilla extract
2 TB barley malt powder (gives the filling a sweet, marshmallowy taste; not to be confused with malted milk powder)
Beat together the shortening and margarine with a handheld beater or stand mixer. Add the powdered sugar and beat until completely light and fluffy, about 5 minutes. Add the vanilla and malt powder and beat for another 2 minutes.
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Again, its not Bavarian cream, but you could sub a non dairy milk and shortening for the butter.
Nonna's Faux Whipped Cream (aka Flour Frosting) - makes enough for 1 9-inch layer or 1 doz cupcakes
1c milk
5TB all-purpose flour
2 tsp pure vanilla extract
1/2 pound room temp butter (2 sticks)
1 1/4 cups granulated sugar (DO NOT use powdered/confectioner's sugar, it contains cornstarch)
In a medium saucepan, whisk milk with all of flour.
Heat mixture over medium heat, whisking constantly until the mixture begins to bubble/sputter.
Continue stirring while mixture thickens. After about 7 minutes of heating and whisking, it should be thick like cake batter.
Stir in the vanilla extract and set mixture aside until COMPLETELY cool.
In the bowl of a stand mixer with the whisk attachment, and med high speed, beat the softened butter with the granulated sugar until mixture is light, fluffy, not gritty, and white in color (about 3 minutes - longer if using a hand held mixer).. Sugar should be totally incorporated.
When milk/flour mixture is completely cooled, add it to the butter/sugar mixture.
Beat everything for about 1 minute on high speed, frequently scraping down the bowl, until the frosting is smooth and well blended.
The frosting should be like whipped cream (light and fluffy).
My only other suggestion is to find a Bavarian cream recipe that uses milk instead of heavy cream and substituting rice milk, almond milk, or soy milk for the dairy milk in the recipe. In theory they should work, but I have never tried it.
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Most people that are casein intolerant can have heavy cream and butter because there are only trace amounts of casein in them.
Casein is found in almost all dairy products, including milk, yogurt, cheese and ice cream. Very high-fat dairy products such as heavy cream and butter contain almost no traces of casein, but very sensitive individuals may react to even trace amounts. Ghee, or clarified butter, is free of casein and is safe even for people with casein allergy. Read ingredient lists carefully to avoid any foods containing dairy-derived ingredients including calcium lactate, sodium lactate, lactic acid and sodium stearoyl lactylate.