Make the crispy caper breadcrumbs. Set a medium skillet over medium heat. Once the skillet is hot, add the olive oil and vegan butter. Let the vegan butter melt and froth a bit before adding the capers and thyme leaves. Stir until the thyme is really fragrant, about 30 seconds. Add the breadcrumbs to the skillet and some salt and pepper. Stir the breadcrumbs frequently until quite browned and crisp, about 3-4 minutes. Set aside to cool.
In an upright blender, combine the sun dried tomatoes and vegetable stock. Blend this mixture until it is completely smooth and smoothie-like in texture. Set aside.
Set a braiser-style pot or a large, deep skillet over medium heat. Once the pot is hot, add the olive oil and swirl it around. Add the shallots to the pot and stir. Cook the shallots, stirring often, until they are very translucent and soft, about 5 minutes. Lower the heat if they start to brown too quick.
Add the garlic and thyme to the pot, season with salt and pepper, and stir until garlic is very fragrant, about 1 minute. Add the tomato paste to the pot and stir it around and cook for a full minute (just to get the tin-y/raw flavour out).
Pour the red wine into the pot and stir. Let the wine bubble up and reduce by half, stirring often.
Once the red wine is reduced, add the white beans and the blended sun dried tomato mixture to the pot. Season liberally with salt and pepper and stir. Bring the mixture to a boil, and then simmer for 15-20 minutes, or until the sun dried tomato mixture has reduced a bit, appears jammy, and is clinging to the white beans.
Serve the jammy sun dried tomato white beans hot with sprinkles of crispy caper breadcrumbs on top and drizzles of olive oil.