It seems you're going for something a little more formal than just tossing the veg in butter or beurre noisette. A beurre blanc might be just the ticket. On top of that, it's what you described.
BEURRE BLANC, WINE-LEMON VARIATION
1 - 3 shallots -- enought to make 2 heaping tbs of finely minced shallot
3/4 cup dry white wine such as a white burgundy or fume blanc
1/2 cup freshly squeezed lemon juice
4 oz (1 stick) cold butter
Salt and white pepper to taste
Put the wine in a sauce pan, and set it over medium heat. Regarding the wine, you want something dry and simple, without too much character. A really oaky chardonnay for instance, won't make a good beurre blanc.
Mince the shallot very fine, and measure 2 heaping tbs into the pan.
Turn the heat up as high as you can but not so high that it spreads beyond the bottom and up the sides of the pan. Bring the wine to a boil and reduce until it's a thick syrupy consistency, i.e., a glace. This means reducing the volume by around 3/4, which in turns means ending up with about 4 tbs (1/4 cup) of reduced wine.
Reduce the heat to a bare boil and add the lemon juice. Reduce the sauce again (slower this time) until it's a syrup. You'll end up with about 5 - 6 tbs total volume. Remove from the heat, AND lower the flame to "low."
Meanwhile, while the lemon and wine reduce, cut a stick of very cold butter into 8 pieces. Hold them in the refrigerator until the lemon and wine are fully reduced.
Add two pieces of butter to the sauce, and return it to the heat. Use a whisk to beat the butter into the sauce. When the butter is half way melted add two more pieces, and beat until they are half way melted. Remove the sauce from the heat and continue to beat butter into it off the piece. Do as before, but one piece at a time, continuing to add a new piece as the preceding piece is half melted. Stop adding butter (between 6 to 8 pieces) when the sauce is thick and silky.
This technique is called "mounting" or monter au beurre in French, and is one of the most important in classic sauce making.
Note that a beurre blanc cannot be held long and will separate after only a few minutes. If you need to hold the sauce longer, you'll want to try a variation with cream called beurre Nantais.
PS. This is an original recipe. If you wish to share it, you have my permission to do so as long as you credit me, Boar D. Laze.