Heat the vegetable oil in a large heavy-bottomed pot over medium heat until shimmering. Add the chopped onion and cook, stirring occasionally, until translucent and fragrant, about 5-7 minutes.
Stir in the minced garlic and smoked paprika, cooking for about 30 seconds until the garlic is fragrant and the paprika turns reddish. Be careful not to burn the spices.
Add the sliced okra to the pot and cook, stirring often, for about 10 minutes until the okra is vibrant green and begins to release its slimy texture, which helps thicken the gumbo.
Next, toss in the sliced shiitake mushrooms and sauté until they are golden brown and slightly crispy around the edges, about 8 minutes. Their deep umami flavor enhances the richness of the dish.
Pour in the vegetable broth, stirring to deglaze the bottom of the pot. Add the diced tomatoes, thyme, and bay leaf, then bring the mixture to a gentle simmer. Let it cook uncovered for about 30 minutes, allowing the flavors to meld and the broth to thicken slightly.
Prepare a slurry by mixing the cornstarch with cold water in a small bowl until smooth. Stir this into the simmering gumbo, then cook for another 10 minutes until the mixture is glossy and thickened, coating the back of a spoon.
Remove the bay leaf and taste the gumbo, adjusting the salt, pepper, and adding a dash of liquid smoke for extra smoky depth. Let it rest off heat for about 10 minutes to allow flavors to deepen.
Stir well before serving, and ladle the hot, thickened gumbo into bowls. Garnish with chopped green onions if desired, and enjoy this comforting, smoky vegan stew.