Preheat the oven to 400 degrees F.
Combine the green beans, capers, pecans, breadcrumbs, coconut oil, Parmesan, lemon zest, shallots and 1/2 teaspoon salt in a large bowl; toss to coat. Pour onto a baking sheet and spread into an even layer.
Bake for 8 minutes. Stir and continue to bake until the beans are just tender and the skins are golden and blistery, about 8 minutes more.