If you're preparing your own artichokes, do this before anything as it takes FOREVER. The method that ended up working for us is microwaving 3 at a time upside-down in a glass bowl filled 1/3 way with water and covered in plastic wrap for about 10 minutes. We removed the very bottom leaves and cut the stem off at the base first, then let cool. Then removed all the leaves, scooped out the fuzzy bits and revealed the hearts (at last!).
Preheat oven to 350F (190C).
Chop your onions and garlic small and saute in a saucepan until translucent, be sure not to burn and try to avoid browning.
While they're cooking quickly peel your chard off the stems and rinse, set aside.
When onions and garlic are almost done, add the artichoke hearts and last tablespoon of olive oil and cook for 3-4 minutes, stirring occasionally.
Add the chard and stir until wilted.
Remove from heat and add to food processer (or blender, but it will be more annoying) with the soymilk. I'd start with 1/4 cup and add more if you think it needs it.
Process until smooth, then transfer back to saucepan with the Tofutti cream cheese, 1/3 cup Daiya, and salt and pepper.
Stir constantly over medium-low heat until everything is all melty and uniform.
Transfer to an oven safe container, top with Daiya (or breadcrumbs?) and bake for about 15-20 minutes, until the Daiya is all melted and toasty.