Sprinkle salt on both sides of the salmon steaks and set a side. (Note: 1/2 teaspoon of salt is the total amount to use for all the salmon steaks)
Thinly slice shallot, ginger and tomatoes. Smash the garlic. Remove seeds from the bird's-eye chili. Set aside.
In a small saucepan, add 2 tablespoons of sugar and 2 tablespoons of water. Bring to a boil, the sugar will fully dissolve. Lower the heat to medium, continue to simmer. You will see that a lot of bubbles on the surface. The mixture will then turn from clear to yellow, and get darker as you simmer it. When it has a honey color, reduce the heat slightly. Keep watching closely, until it has a dark caramel color, turn off the heat and carefully add 1 tablespoon of water. Swirl the saucepan to combine (add 1/2 - 1 more tablespoon of water if the caramel sauce is too thick) and remove it from the stove. Set aside.
In a pan over medium high heat, sear salmon steaks for 2-3 minutes each side or until golden. Transfer them to a plate.
Place a pot that can fit all the salmon in a single layer on medium heat. Add oil and sauté shallots for a few seconds Add garlic and ginger and sauté for a few more seconds until fragrant. Arrange them to cover the bottom of the pot and place tomato slices on top. Place salmon steaks on top of the tomatoes.
Add 1 1/2 cups of water or enough to cover the fish, add fish sauce, caramel sauce and bird's-eye chili and bring to a boil. Lower to a simmer (low - medium low heat). Sprinkle plenty of black pepper and simmer 10 minutes then gently flip the fish. You can taste the braising liquid and adjust to taste, but remember it will get saltier as we continue cooking and reduce the liquid further.
Continue to simmer for 20-30 minutes, flip the fish one (or two) more time. Occasionally spoon the braising liquid over the salmon. If the liquid reduces too rapidly, you can add a little more water. In the last 5-10 minutes of cooking, watch closely because it may burn. The liquid will reduce, thicken like a sauce. Turn off the heat when there's just enough sauce to coat the bottom of the pot (or sooner if you prefer more sauce).
Transfer salmon to a shallow serving bowl and sprinkle some more black pepper. Serve with rice.