The best way to address this issue will be to build a series of dams from downed
trees and branches.
As others have mentioned you don't want to stop the flow but rather filter the flow, letting any sediment drop out when the flow slows enough.
once you have these established you can then begin to do the bank stabilization with
straw mats that you coat with grass and other plant seeds.
These mats can be formed from round bales (hay instead of straw) and held in place with twine and stakes, hay has the advantage of already having some residual seeds.
The dams can start out at a low height which you then build up as you come across more materials.
I am doing this on our north facing slope that was forming a gulley from rain
runoff.
At the bottom of the slope I am building a small pond by filling in the current gully and building along the bank upper edge with the exposed rocks from the erosion.
I have short dams at 10 foot intervals from the ridge all the way down to the pond structure.
Redhawk