Trim the stem ends of the collard greens. Stack the leaves on top of each other, one bunch at a time, and cut crosswise into 1-inch-wide strips; set aside.
Heat a large 12-inch skillet, preferably cast iron, over medium-high heat. Add the oil and heat for 1 minute. Add the onion and garlic and sauté, seasoning with 3/4 teaspoon of the salt, 1/2 teaspoon of the pepper, and crushed red pepper halfway through cooking, until soft and slightly brown, 7 to 10 minutes total.
Add the collards in handfuls, tossing to wilt, for 2 to 3 minutes. Stir the onions and collards until fully combined. Add the broth and cook, stirring occasionally, until the greens are soft and the liquid has mostly evaporated, 15 to 20 minutes.