Combine the daikon, carrots, apple, scallions, onion, ginger, dulse flakes, vegan fish sauce, coconut sugar, water, and salt in a large stockpot. Bring to a rolling boil over high heat and then decrease the heat to a steady simmer for 60 minutes.
Strain the broth through a wire-mesh sieve and return the clear broth to the pot.
Warm the olive oil in a separate pot over medium heat. After 90 seconds when the oil is hot, add the shallot and cook for 3 minutes.
Add the tomatoes, bird’s eye chilies, and anatto powder. Stir-fry for 4-5 minutes over medium heat until the tomatoes start to break down.
Add the tamarind concentrate and stir-fry for 1 minute. Pour the strained broth into the pot and bring to a simmer over medium heat for 10 minutes.
Cook the rice vermicelli according to package directions. Rinse under cold water and drain well.
Add the beech mushrooms, vegan ham, and tofu puffs to the simmering broth. Cook for 5 minutes over medium heat.
Divide the noodles among serving bowls. Ladle the hot broth, mushrooms, vegan ham, and tofu puffs over the noodles. Serve with Thai basil leaves, sliced bird’s eye chilies, perilla leaves, scallions, and lime wedges.