Set a small sauté pan over medium heat. Once the pan is hot, pour in the teaspoon of olive oil and swirl it around. Add the shallot, chili, and garlic to the pan and stir. Keep sautéing until there is some slight browning and the shallots are soft, about 5 minutes.¼
Add the paprika and nutritional yeast to the pan and stir. Keep stirring and cooking until spices are fragrant. If spices are sticking to the bottom of the pan and browning too quickly, simply add a splash of water to loosen everything up. Once you've done that, take the pan off the heat and allow it to cool slightly.
Add the sautéed shallot and spice mixture to an upright blender, along with the drained cashews/sunflower seeds/sliced almonds, roasted red pepper, water, lemon juice, tomato paste, white wine vinegar, Dijon mustard, coconut aminos, some salt and pepper, and the remaining ¼ cup of olive oil.
Blend the mixture on high until completely smooth and creamy, about 1-2 full minutes. If you need to stop the blender's motor to scrape down the sides with a spatula, go right ahead! Similarly, if you're finding that the blades don't have enough liquid to get going, add additional water to the blender, 1 tablespoon at a time, until you can get it all moving.
Taste the dip to check it for seasoning. You may want more salt, more acidity in the form of lemon juice or vinegar, more spice, more nutritional yeast etc! Adjust to your liking if needed and blend it one more time.
Serve the vegan red pepper dip with a swoop of olive oil on top, a sprinkle of paprika, and some chopped herbs if you like. The dip keeps in a sealed container in the fridge for about a week.