Set the whole bell peppers on a rimmed baking sheet. Slice the top off the head of garlic, drizzle with 1 tablespoon olive oil, wrap tightly in foil, and add to the sheet. Roast 35 to 40 minutes, turning the peppers once or twice, until the skins are blackened and collapsing and the garlic is soft.
Transfer the hot peppers to a bowl, cover tightly, and steam 10 minutes to loosen the skins. Set the garlic aside to cool.
While the peppers steam, toast the almonds in a dry skillet over medium-low heat, shaking often, 4 to 5 minutes until golden and fragrant. Transfer to a plate.
In the same skillet, toast the panko in 1 tablespoon olive oil over medium heat, stirring constantly, 2 to 3 minutes until golden. Season with a pinch of salt and set aside.
Peel the skins off the cooled peppers with your fingers and remove the stems, cores, and seeds. Don't rinse them or you'll lose the smoky flavor. Add the flesh to a food processor.
Squeeze in the roasted garlic. Add the almonds, torn bread, sherry vinegar, smoked paprika, salt, pepper, and 2 tablespoons olive oil. Blend until mostly smooth but still slightly textured, then drizzle in the last 2 tablespoons olive oil with the motor running. Taste and adjust. The sauce should be thick and spoonable.
Boil a large pot of salted water and cook the rigatoni until al dente, usually 11 to 12 minutes. Reserve ½ cup pasta water, then drain.
If pairing with halloumi, while the pasta cooks, sear the halloumi in 1 tablespoon olive oil over medium-high heat, undisturbed, 2 minutes per side until deeply golden.
Return the drained pasta to the pot off heat. Add about 1½ cups romesco and ¼ cup pasta water and toss until every piece is coated, adding more pasta water a tablespoon at a time if it looks dry. Save the rest of the sauce for another use.
Divide among 4 plates. Top with the halloumi, toasted breadcrumbs, basil, grated Pecorino, a drizzle of olive oil, and flaky salt. Serve immediately.
Notes
Halloumi is optional but adds a salty, chewy protein. If you skip it, add an extra tablespoon of grated Pecorino at the end.
For gluten-free, use GF pasta, skip the bread and breadcrumb topping, and add 2 extra tablespoons almonds to the sauce.
This makes extra sauce. Use leftovers on eggs, vegetables, toast, or potatoes.
Make the sauce ahead and refrigerate until ready to use.
Leftover pasta keeps 3 days; sauce keeps 5 days and freezes well for 2 months. Reheat with a splash of water and olive oil to loosen.