Step 1

Heat oil in a large skillet over medium-high. Add onion, mushrooms, and thyme; season with salt. Cook, stirring occasionally, until mushrooms are browned, 10 to 12 minutes. Add spinach; cook 2 minutes more. Add vinegar and 1/3 cup cream. Cook, scraping browned bits from bottom of skillet, 1 minute. Let cool completely.

Step 2

Preheat oven to 425 degrees. Cut a slit down length of each tenderloin, deep enough to reach center, and season with salt. Pack mushroom mixture evenly into slits, then reshape tenderloins into logs with your hands, enclosing filling as much as possible.

Step 3

Unfold pastry on a lightly floured work surface. Roll out to an approximately 13-inch square; cut in half. Starting at one short end of each piece, score diagonal lines, 1 inch apart, with a sharp knife or pizza wheel (do not cut all the way through). Score in other direction, creating a crosshatch pattern. Transfer both doughs to a parchment-lined rimmed baking sheet, scored-sides down (if they become too soft, chill briefly). Divide prosciutto evenly between doughs, overlapping to fit and leaving 1-inch borders of dough. Center a tenderloin on top of each dough, stuffed-sides down. Whisk egg with 1 teaspoon water; brush borders with egg wash. Lift long sides of each dough up and over pork, stretching slightly as necessary until edges meet; pinch edges to seal. Fold short sides up over pork and flip so seams face down. Brush all over with egg wash; cut a few 1-inch vents in tops. Refrigerate 30 minutes.

Step 4

Bake until pastry is puffed and golden brown and a thermometer inserted into centers of pork registers 140 degrees, 20 to 25 minutes. Transfer Wellingtons to a wire rack; let cool 15 minutes. Meanwhile, stir together mustard, remaining 1/3 cup cream, and 2 tablespoons water; season with salt and pepper. Slice Wellingtons into 2-inch rounds and serve with mustard sauce.