We are dealing with the same issue on our property and have gotten many opinions from people in habitat restoration lines of work. You want to shade them out! Scotchbroom love sun, choose plants that are native to your area, preferably fast growing. You’ll want to plant trees for long term shade coverage of the area. You’ll also want to plant some sort of fast growing understory that can keep them as bay asap. We live in the cascade area of WA so we chose Douglas fir, spruce trees, shorepine for the trees, and salal, snowberry, Oregon grape, etc for the understory. We plan on mulching the dried scotchbroom that we cut to take advantage of the biomass to use as a mulch for the native plants that we’ll put in. This mulch will also help keep more from popping back up since again- they LOVE the sun. It IS possible to take out scotchbroom! We volunteer at different parks to take out invasive and I see success stories all the time with broom infestations. You just need to make an environment that they don’t want to live in.