Toss the dark scallion parts into a medium saucepan with a thin slice of lemon. Add the wine, ¹⁄₂ cup water, and a pinch of salt; bring to a boil. Add the salmon fillet; reduce to a simmer, cover, and cook 1 minute. Remove the pan from the heat; set aside (covered) for 10 minutes. Transfer the salmon to a plate and refrigerate for 20 minutes or up to 1 day (cover if refrigerating overnight). Discard the cooking liquid.

In a medium bowl, beat the butter with a flexible spatula until spreadable. Add the grated zest of the lemon, the juice from half the lemon, the minced scallions, shallot, a pinch of salt, and 2 pinches black pepper; stir thoroughly. Stir in the smoked salmon.

In a small bowl, combine the mayonnaise, mustard, capers, honey, 1 ¹⁄₂teaspoons lemon juice, and a pinch of black pepper; add to the smoked salmon mixture. Stir well to combine.

Remove the cooked salmon from the fridge and cut into bite-size pieces. Gently stir into the smoked salmon mixture, keeping the pieces as chunky as possible. Taste and adjust the salt, pepper, and lemon juice if needed. Fold in the chopped dill and cilantro.

Transfer the rillettes to a serving bowl or jar. Serve immediately, or preferably cover and refrigerate 6 hours or up to 3 days. Serve with sliced baguette or crackers.