Preheat a grill to medium high. Toss the okra and green beans with 2 tablespoons olive oil; season with salt and pepper. Transfer to a sheet of foil or a grill basket with the okra cut-side down. Grill the vegetables, turning occasionally, until lightly charred and tender, 6 to 8 minutes.
Transfer to a cutting board. Halve the beans crosswise and halve any large okra pieces lengthwise.
Meanwhile, heat the remaining 2 tablespoons olive oil in a small skillet over medium heat. Add the panko and cook, stirring, until golden, 2 to 4 minutes. Remove from the heat and stir in the lemon zest; season with salt and pepper.
Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs for al dente. Reserve 3/4 cup cooking water, then drain the pasta and return to the pot. Stir in the grilled okra and green beans, parmesan and garlic, stirring in enough of the reserved cooking water to loosen. Stir in the basil. Divide among bowls and top with the panko mixture.
Photograph by Ryan Dausch