Preheat broiler to 400 degrees F. Place cauliflower steaks onto a baking sheet. Drizzle with 2 TBS melted butter or oil and sprinkle with a tsp of salt. Roast for 15-25 minutes, when the cauliflower is dark golden brown on the edges. Remove from oven and set aside to cool.
Heat 5 TBS oil/butter in a large pot over medium heat. Add onion and garlic and cook, stirring often, until softened and beginning to brown, about 5 minutes. Meanwhile, drain and rinse the hearts of palm very well. Add Hearts of Palm; season with about 1/2 tsp salt and pepper. Cook, stirring occasionally, until Hearts of Palm is softened and beginning to brown, about 8 minutes. Remove the pieces of Hearts of Palm and set aside.
In the stock pan (that you just removed the Hearts of Palm from), add the reserved cauliflower, thyme sprigs and 5 cups broth to pot. Bring soup to a boil, reduce heat, and simmer until cauliflower is very soft, about another 8 minutes; discard thyme sprigs. Purée the cauliflower soup mixture in a blender until smooth. Transfer soup to a large bowl, add the reserved Hearts of Palm, cover, and chill until cold, at least 2 hours.