Put the potato and carrot in a small pot and cover them with water by about an inch. Add a pinch of salt, bring the water to a boil, then lower the heat and simmer for 10 to 12 minutes, until both vegetables slide off a fork without resistance.

Drain the vegetables, but save about 1/2 cup of the cooking water first. Transfer the potato and carrot to a blender.

Whisk the cornstarch into 1/4 cup of the oat milk until there are no lumps left. Add that mixture to the blender along with the remaining oat milk, vegan butter, nutritional yeast, tomato paste, lemon juice, smoked paprika, cumin, garlic powder, onion powder, salt, and turmeric.

Blend on high for a full 60 seconds, until the sauce is completely smooth and you can't see any flecks of potato or carrot. Add a splash of the reserved cooking water if the blender struggles to move.

Pour the blended sauce into a saucepan and set it over medium heat. Cook for 3 to 5 minutes, stirring constantly with a spatula, until it thickens enough to coat the spatula and just begins to bubble at the edges.

Stir in the chopped pickled jalapenos and a teaspoon of their brine. Taste and add more salt, lemon juice, or brine as needed, then serve warm.