Combine the porcini and boiling water in a small bowl. Let sit until the mushrooms are softened, about 20 minutes. Lift the mushrooms from the liquid, rinse well to remove any remaining grit, and pat dry. Strain the liquid through a coffee filter or paper towel-lined sieve to remove sediment, then reserve the specified amount for the pâté.

Pulse the white mushrooms and rehydrated porcini in a food processor until they are finely chopped and uniform but not pureed, about 10 to 12 pulses.

Melt the butter in a large skillet over medium-high heat until the foaming subsides. Add the chopped mushroom mixture, shallots, and a pinch of salt. Cook, stirring occasionally, until the mushrooms have released their liquid and the pan is dry, 8 to 10 minutes.

Stir in the garlic and thyme and cook until fragrant.

Stir in the reserved porcini soaking liquid, cream cheese, and heavy cream. Cook over medium heat, stirring constantly, until the liquid is absorbed and the mixture is thick and creamy, about 2 minutes.

Remove from the heat and stir in the parsley and lemon juice. Season with salt and pepper to taste. Serve warm or at room temperature with crostini or crackers.