Bring a large pot of well-salted water to a boil.
Toast the almonds in a dry pan over medium heat for 2-3 minutes, stirring often, then let them cool slightly.
If the sun-dried tomatoes are very salty, rinse them quickly and pat dry.
In a food processor, blend almonds, Parmesan, Pecorino, garlic, and lemon zest until finely chopped.
Add the sun-dried tomatoes and basil, then pulse again until the mixture becomes thick and rustic.
With the machine running, slowly drizzle in the olive oil. Add a little pasta water to loosen the pesto until creamy and spoonable. Season with black pepper. Taste before adding salt.
Cook the bavette until al dente according to the packet time.
Reserve at least 180 ml / 6 fl oz of pasta water, then drain the pasta.
Transfer the bavette to a large pan or bowl. Add the pesto and a splash of reserved pasta water. Toss gently until every strand is glossy and evenly coated.
Add a little more pasta water if needed to create a smooth, silky sauce. Plate immediately.