Add the almond milk a little at a time while continuing to beat, until the glaze is still thick but able to drizzle slowly off the end of a spoon and leave a trail in the bowl (i.e. it doesn't immediately get absorbed back into the rest of the glaze).
2 tablespoons milk
Once the cake is baked, cool for about 10 minutes and then invert the bundt pan onto a serving plate to remove the cake. Drizzle the glaze over the cake just prior to serving. Sprinkle with chopped pecans for garnish if desired.
½ cup chopped pecans
Notes
If you would like to use non-dairy milk, use one cup of your alternative milk instead of one cup of regular milk. I think a vanilla almond milk would work really well. Note that you may need to add a little sugar as well if you use a non-sweetened non-dairy milk.
You can make this ahead of time and freeze it. Freeze the cake after it is baked and cooled, but don't prepare the glaze until you are ready to thaw and serve the cake. Make sure you take the proper precautions to prevent freezer burn, such as using a good storage container.
If you are feeding a crowd, you may want to double this recipe. I haven't tested this variation specifically, but it is likely you will need to increase the baking time. I recommend increasing it to 30 minutes and then checking it to see if it needs even more extra time.
If you are looking for a smaller sized dessert, you may be tempted to try cutting this recipe in half. I wouldn't really recommend that, as the cake will be really little and I think it would get dried out. It might be a better idea to make the whole recipe, and then cut the cake in half after it is baked and cooled, and store the half you aren't going to use in the freezer.
If you are looking for something gluten-free or vegan, I would recommend searching for cake recipes that are developed with those dietary constraints already in mind. My apologies, but since I am not an expert in either of those areas, I am not really able to give you the best way to make those substitutions.