Bring a large pot of water to a boil for the pasta.
Heat a small skillet over medium. Add the sliced almonds and cook, stirring often, until toasted, 3 to 4 minutes. Transfer to a cutting board and let cool. Finely chop the nuts. Return the skillet to medium heat and add the butter. When the butter melts, add the panko and cook, stirring often, until golden brown, about 2 minutes. Transfer to a small bowl; mix in the almonds and herbs. Season with salt and pepper.
Meanwhile, halve the cherry tomatoes. (If using tomatoes on the vine, prepare a large bowl of ice water. Score an X on the bottom of each tomato, add to the boiling pasta water and cook until the skin around the X begins to peel back, about 30 seconds. Transfer to the ice water; let cool about 1 minute. Pat dry, then peel and chop. Return the water to a boil.
In a large skillet, heat the olive oil, three turns of the pan, over medium-high. Add the garlic; swirl a minute or two. Add the tomatoes; season. Cook, occasionally shaking the skillet, until the tomatoes break down, about 10 minutes.
Salt the boiling water, add the pasta and cook until 1 minute shy of al dente. Reserve half a mug of the starchy cooking water, then drain the pasta.
Add the lemon zest and juice, the basil, pasta and cooking water to the tomato sauce. Drizzle with EVOO and toss until combined, 1 to 2 minutes; season with salt.
Serve the pasta in shallow bowls topped with the nutty breadcrumbs and the cheese.
Everything You Need to Know About Pasta Water