Tarragon Cream sauce Pasta

I'm telling Esme about another one of the family recipes that I want to make and show her how to make - and every other recipe I've been finding for it uses white wine in it for reduction in the sauce. And I had to think, ah.. yes, my mother never cooked with that (cooking alcohol) at all, so of course the 'family recipe' that I know doesn't have it, so.. do I try to do it 'correctly' according to the books or do I cook what I know so I don't 'mess it up'? I'm choosing option two, and then maybe we can learn how to make the 'actual French recipe version' later.  Apparently there is a 'boil the onions in white wine' step that I've never done in my life.. and am not sure I want to.  

 This is usually served with chicken breast, but can also be served with eggs.  We didn't have fresh garden tarragon, but I was inspired to make this by the dried tarragon packet I got in our spice sampler.  Tarragon goes bad quickly, much quicker than many spices - and the reason I haven't made it in many years is that it is hard to find it, and then when you do, a little disappointing to throw much of it away later.  I used finely diced zucchini instead of the real chopped tarragon plants that were in a recipe I found - I think maybe it was made with canned green beans at times in our household, my mom canned a lot of green beans every summer.

 We decided to make it with eggs.  It is not an easy dish to make with three burners by yourself - will need to practice again, as one of the burners was an omelette to go with it and that got a bit messy in between - started pasta, then melted butter in a big pan and added finely diced zucchini and sliced sweet onions, cooking them until the onions were translucent, then added a bit more water to make sure there was enough liquid - added a few tablespoons of flour until it began to form a paste with the butter, added some grated cheese (used the last of the gruyere block we had, about 3 by 2 inches) to that to finish making it a full paste (roux), then began to reliquify with half-and-half, then whole milk, until the sauce and melted cheese came to the right consistency, added dried tarragon and lots of black pepper (should have added more salt, I had hoped the butter and cheese was salty enough) and removed from heat as the omelette was getting done to put on the plates and drained the pasta, stirred it into the tarragon cream sauce and added more black pepper and shredded cheese on top of each plate after serving. It's been years, maybe a decade, since I made this dish, but I thought I'd give it a go again to show Esme.