To prepare the lemongrass, start by peeling off any very dry layers and slicing off the very end of the stalk. Thinly slice the next 2 to 3 inches of the bottom of the stalk (enough for 2 tablespoons), then chop the slices up finely. You'll only use the bottom of the stalk, not the top. Use 1 tablespoon of chopped lemongrass in the marinade and save the other tablespoon for when you're cooking.
Mix the marinade ingredients together, then toss it with the chicken (or other protein) until thoroughly coated, either in a freezer bag or a large bowl. Leave the chicken to marinate in the fridge, still in the bag or bowl, for 2 to 3 hours or overnight.
Once the chicken has marinated, put some oil in a large pan over medium heat. Add the remaining lemongrass and stir fry for 30 seconds or so. Add the shallot and cook for about a minute, until it starts to turn translucent. Then add the garlic and cook for another minute.
Turn up the heat to medium-high and add the chicken all at once along with the marinade sauce. Try to make sure all the chicken is touching the pan so it can get browned. Leave for about 2 minutes, until that side of the chicken is cooked and a little browned.
Flip the chicken and cook for another 2 minutes on the other side.
Add enough broth to almost cover the chicken in the pan. Cover with a lid and cook for about 5 minutes, until the sauce thickens and everything is cooked through.
Serve over rice (maybe fried rice) or in a wrap with cooked vegetables like green beans, pea pods, or carrots.