Heat a small skillet over medium heat. Add the walnuts and toast, stirring frequently, until fragrant and lightly golden, about 4-5 minutes. Watch closely - they burn fast. Transfer to a plate to cool.

Position a rack 6 inches from the broiler and heat to high. Place the tomato halves cut-side up and the smashed garlic on a baking sheet. Broil until the tomato is charred and collapsed and the garlic is deeply golden, about 8-10 minutes. Let cool slightly.

In a food processor, combine the toasted walnuts, roasted red peppers, broiled tomato, garlic (remove any overly charred bits if bitter), smoked paprika, and sherry vinegar. Pulse until a coarse paste forms, scraping down the sides as needed.

With the processor running, slowly stream in the olive oil until the sauce is smooth and creamy but still has some body - you're aiming for the texture of loose hummus. Add the salt and cayenne if using, then pulse to combine. Taste and adjust salt or vinegar as needed.

Transfer to a bowl and let sit at room temperature for at least 15 minutes before serving, or refrigerate for up to 5 days. Bring to room temperature and stir before using - the oil may separate slightly.