In a large saucepan, cover potatoes with water and bring to a boil. Reduce heat to a low boil and cook until a knife inserted slides off easily.
In the meantime, add the cauliflower to a strainer or veggie steamer and place on top of the potatoes in the saucepan to cook at the same time. Cover with a lid to steam.
Once both are soft and cooked through, transfer to a bowl and mash with a potato masher, adding salt and pepper and 1 Tbsp of vegan butter to season. Set aside and cover to keep warm.
In skillet over medium to medium-high heat, melt the vegan butter. Add the shallot and mushroom and cook for 10 minutes, stirring frequently. Cook until the mushrooms are soft and brown, and most of their liquid is evaporated.
Stir in the flour with a whisk and reduce heat to medium. Cook for another minute or two.
Slowly add veggie broth while whisking to reduce clumps. Then add in the thyme and whisk again.
Reduce heat to simmer and continue to stir until it reaches desired thickness – about 5-10 minutes. If it appears too thin, add a touch more flour and whisk. If it’s too thick, add more broth.
Season with salt and fresh ground black pepper to taste. Serve over cauliflower mashed potatoes. Store leftovers in the fridge in an air-tight container for up to a few days.