Separate the spring onion tops from the bottoms. Slice the onion bottoms in half lengthwise, then toss with a little neutral oil and kosher salt.
Place the spring onion bottoms on a hot grill or grill pan and cook until deeply charred, softened, and caramelized. Let cool slightly, then finely chop. You should have about 1 cup of grilled spring onion bottoms.
Bring a pot of salted water to a boil. Add the spring onion tops and spinach, then blanch for about 30 seconds, until softened and bright green. Drain well.
Blend the blanched spring onion tops and spinach with neutral oil and a pinch of salt until smooth and vibrant green.
Add the room temperature butter to a large bowl. Mix in the chopped grilled spring onions, green onion spinach puree, fresh tarragon, kosher salt, and black pepper.
Whip the spring onion compound butter until light, fluffy, and fully combined. Taste and adjust seasoning as needed.
Transfer the spring onion butter to a container. Refrigerate for up to 1 week or freeze for up to 1 year.
Season the steak generously with kosher salt and black pepper. For tri-tip, salt ahead of time and let it sit uncovered in the refrigerator to help dry the surface and build a better crust.
Heat a pan or grill over high heat with a little neutral oil. Sear the steak until deeply browned and cooked to your preferred doneness. Rest before slicing, and reserve the pan drippings for the mushroom sauce.
Add the maitake mushrooms to the same pan used for the steak. Cook until the mushrooms release their moisture, then continue cooking until deeply golden brown and caramelized.
Add the rice wine vinegar and scrape up the browned bits from the bottom of the pan. Reduce until nearly dry.
Stir in the Dijon mustard, beef stock, and reserved steak drippings if using. Simmer until the mushroom pan sauce is glossy and slightly thickened.
Turn off the heat and whisk in the butter while shaking the pan to emulsify the sauce. Season with kosher salt to taste.
Slice the steak and spoon the mushroom pan sauce over the top. Add a generous spoonful of spring onion steak butter directly onto the hot steak so it melts into the meat.
Serve with grilled onions, roasted potatoes, toast, or vegetables.