Make Sauce: Combine Gochujung Sauce ingredients in a small bowl or mason jar. Whisk and/or shake to fully combine. Set aside.
Cook Veggies: Bring large cast iron skillet to medium-high heat. Add ½ tablespoon extra virgin olive oil; swirl to coat bottom of the pan. Add carrots and move around pan, approx. 5 minutes. Add onion and zucchini (add more olive oil, as needed). Move around pan until zucchini is soft, but firm. Season with kosher salt and ground black pepper. Transfer to bowl; set aside.
Cook Beef: In the same cast iron skillet add 1 pound ground beef. Break apart and move around pan until fully cooked. Strain excess grease and return pan to stovetop. Season with kosher salt and ground black pepper and 2 teaspoons garlic. Move around until garlic is fragrant. Add approx. 1/3 of the Gochujung Sauce. Stir to combine with the ground beef.
Build Bowl: Divide rice between either 2 or 4 bowls. Top with cooked veggies and ground beef. Top with poached egg, fresh cracked pepper, and plenty of the remaining Gochujung Sauce.
Notes
Ground Beef: feel free to use a different ground meat here such as ground turkey, if you prefer.