1. To make the romesco, preheat the oven to 375°F (190°C). Spread the almonds on a large, heavy-duty baking sheet and toast in the oven, stirring once or twice, until fragrant and slightly darkened, about 10 minutes. Remove from the oven and immediately pour onto a plate to cool; the nuts can burn easily. Leave the oven on.
2. On the baking sheet, toss the tomatoes, bell peppers, onion slices, and garlic cloves with the 2 Tbsp olive oil and 1 tsp salt. Roast until all the vegetables are tender and slightly charred, 15-30 minutes. As each vegetable is done, transfer it to a bowl. The onions and garlic will cook first, followed by the peppers and then the tomatoes.
3. When all the romesco vegetables are done, transfer them to a blender or food processor. Add the vinegar, paprika, and cayenne and process to a smooth purée. Taste and adjust the seasoning. Set the romesco aside.
4. Clean off the baking sheet, then add the root vegetables and toss with the 2 Tbsp olive oil and 1 tsp salt. Spread the vegetables in a single layer and roast until tender and nicely caramelized, about 40 minutes. Arrange the roasted root vegetables on a platter and pour the romesco sauce over them. Serve right away.