Combine oyster sauce, soy sauce, brown sugar, fish sauce and pepper in a bowl. Mix well and set this sauce aside.
Peel the chayote squash, remove the core then thinly slice it.
Peel and thinly slice the carrots.
Place 1 tsp oil in the saucepan and cook the carrots for 3-4 minutes. Then remove the carrots from the pan.
Using the same pan, add more oil then add the thinly sliced chayote squash. Cook for 3-4 minutes.
Add the carrots back into the pan with the chayote squash.
Pour the sauce on top of the vegetables. Toss to combine and it's ready to serve.