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 the liquid smoke, and cook, stirring occasionally, until the greens are soft and the liquid has mostly evaporated, 15 to 20 minutes.