To make the sauce, whisk together sesame oil, garlic, ginger, soy sauce, coconut sugar (or brown sugar), chicken broth, arrowroot flour and lime juice. Set aside.
Slice the Filet into 1/4 inch thick, bite-size pieces. Place into a shallow dish and pour 1/2 cup of the sauce over the steak to marinate. Set aside.
While that sits, dice the onion and peppers into a large dice and cut the broccoli into florets
Heat a large cast iron, or nonstick, skillet to medium high heat.
Start a pot of boiling water so it's ready for the ramen.
Add 1 Tbsp olive oil to the heated skillet. In 2 batches, place the slices of meat onto the skillet and cook for 1-2 minutes per side until all the beef is browned and cooked through (adding more oil if needed between batches).
Remove the beef and set aside.
Lower the heat to medium and add about 1 Tbsp more olive oil.
Saute the onion and bell peppers for about 2 minutes until they start to soften.
Add in the broccoli florets and cook for about 5 minutes until all of the veggies are softened. Add 1-2 Tbsp of the sauce to help cook the broccoli through.
While the veggies cook, boil the ramen according to the package instructions.
While your large skillet is on low heat, add in the beef, remaining sauce, and the cooked ramen noodles.
Simmer and stir, using tongs, until the noodles, veggies, beef, and sauce are combined.
Serve with scallions to garnish.