Pulse the almonds in a food processor for a few seconds until they're roughly chopped.
Add the tomatoes, parsley, basil, garlic, chili and salt and pulse to a rough paste. Add the olive oil and continue to process until the sauce is like crunchy almond butter - you want small pieces of almond in there so don't go overboard.
Transfer the pesto to a large serving bowl and stir in the cheese.
Make the pasta
Bring a large (5- 6 quart) pot of water to a boil. Season with 3 tablespoons salt.
Cook the pasta until it's al dente. Scoop out 1 cup of the pasta cooking water and reserve. Drain the pasta.
Mix ½ cup of the pasta water into the pesto until it forms a creamy, saucy consistency, adding more water a little at a time if it's too thick. Add the hot pasta to the bowl and toss with the sauce.
Tear the burrata into pieces and distribute over the pasta (it will be too soft to slice). Sprinkle the pasta with a little more grated Romano cheese and some of the herb leaves, if you like.
If you don't have bucatini, this pesto sauce would be great on rigatoni or even spaghetti.
Buffalo or fresh mozzarella balls make an excellent substitute for burrata cheese.