Pulse the bread and 1 teaspoon oil in a food processor to make coarse breadcrumbs.
Heat the remaining 2 tablespoons oil in a wide, shallow pot over medium-high heat. Add the shallots, garlic, cumin and cayenne and cook, stirring, until softened, about 2 minutes. Add the collard greens and 1/2 teaspoon salt and cook, tossing with tongs, until mostly wilted, about 5 minutes. Add the cream and chicken broth and bring to a simmer. Simmer, stirring occasionally, until the collard greens are crisp-tender and the liquid is slightly thickened and reduced, abut 5 minutes.
Transfer the greens and liquid to a shallow 1/2-quart gratin dish. Top with the breadcrumbs and crumbled feta. Bake until the crumbs are golden brown, 10 to 15 minutes.