Preheat the oven to 400 degrees Fahrenheit (200 Celsius)
Thinly slice the leek’s stalk, and wash it thoroughly.
In a large pan, melt the butter and add the salt and leeks. Cook on low heat, stirring every few minutes, until very soft, about 30 minutes. (For normal melted leeks, you would cook them longer - but these will cook more under the salmon.)
Meanwhile, make the honey teriyaki sauce. In another pan, heat the sesame oil and add the grated ginger. Cook over medium heat until fragrant, 20 to 30 seconds.
Add the honey to the pan with the grated ginger and cook until it melts, then add the soy sauce and rice vinegar.
Simmer over medium-high heat, stirring every few minutes, until it noticeably thickens and leaves a thin but viscous layer on the back of a spoon that doesn’t fill in after you run your finger through it. This should take about 20 minutes.
Prepare your salmon. Drizzle olive oil into a baking dish, then make leek beds for each piece of salmon. Place the salmon onto the leek beds, skin-side down. Brush a generous layer of honey teriyaki glaze over the salmon.
Bake the salmon at 400 degrees Fahrenheit for about 5 to 6 minutes per ½ inch of thickness (height from top to bottom, not the width from side to side). The nice fat pieces pictured took about 18 minutes.
Halfway through the baking time (which depends on the thickness of your salmon), brush the fillets with another layer of glaze.
When your salmon is done, brush it with teriyaki glaze one more time. Serve with the melted leeks, which will have absorbed some of the glaze drippings. Yum!