Make the sauce. In a small bowl or jar, add coconut aminos, broth, lime juice, honey, sesame oil, garlic, ginger, red pepper flakes, and pepper and whisk to combine. In a separate jar, make a slurry by adding 2 tablespoons broth along with the arrowroot flour and whisk to combine. Set both of them aside.
Cook ramen. Bring a large pot of water to a boil and cook ramen according to the package instructions. Once al dente, drain. When draining, reserve 2 tablespoons of pasta water. The noodles do not take long to cook, so try to plan them being done when everything else is about done (I usually put them in the water when starting to cook the sauce).
Cook the beef. Heat a large skillet or nonstick pan over medium heat, add oil, and let it get hot. Add ground beef, breaking it up with a spatula or meat chopper. Season with salt and pepper. Cook for 5-6 minutes until browned on the outside and cooked through. Remove from the skillet (leaving the juices behind) and set aside.
Saute the veggies. Leaving the beef juices in the pan, add broccoli, mix well, and cover with a lid. Cook for 3-4 minutes. If needed you can add a little broth to the pan, depending on on how much beef juice you have left. Add mushrooms and a pinch of salt and pepper, stir to combine, and saute for 4 minutes, stirring occasionally. Remove veggies from the pan and set aside (leave behind any juices).
Thicken the sauce. Turn the heat down to medium-low and let the pan cool off for 30-60 seconds. Give the slurry another good whisk to make sure there are no clumps. Add sauce and the slurry to the pan, whisking to combine. Turn the heat back up to medium and cook until thickened and it coats the back of a spoon (a nappe consistency), about 3-5 minutes.
Drain noodles, saving 2 tablespoons of pasta water.
Assemble. Add the noodles, beef, and veggies back to the skillet, toss to combine, and heat through for about 1 minute. If desired, add a little pasta water.
Enjoy! Garnish with toppings of choice and enjoy!