Bring a large pot of salted water to a boil over medium heat. Blanch collards until bright green, about 1 minute. Transfer immediately to an ice bath to shock, saving the boiling water for cooking the pasta. Remove the collards from the ice water and pat dry with paper towels before transferring them to a food processor.
Add the linguine to the pot of salted boiling water and cook according to package instructions.
Meanwhile, in a dry skillet, over low heat, toast the pecans until fragrant. Transfer to the food processor with Parmesan, olives and garlic. With food processor running, slowly drizzle in olive oil until pesto comes together. Taste for seasoning, and add salt and freshly ground black pepper, to taste.
To serve, put enough pesto to coat the pasta into a large serving bowl. Drain the pasta and quickly add it to the bowl. The water still clinging to the pasta will loosen up the pesto. Toss to coat. Add more pesto, if needed. Transfer the pasta to a serving bowl and garnish with Parmesan sprinkled over the top.