Champagne is nowadays very often consumed "raw", i.e. very little sweetened (to be "raw", a Champagne must have less than 12 grams of sugar per litre). Served with a dessert, which is by definition sweet, you can experience an unpleasant feeling of acidity (which can be described as "green").
Try it and offer the same Champagne Brut as an aperitif with a parmesan tile, it will be 100 times more appreciated!
If you absolutely want to combine your dessert with Champagne, you can choose either Champagne Rosé on red fruit pies or "dry" or "semi-dry" Champagne (which will be much sweeter than Brut) on a so-called classic dessert.
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