In a sauté pan over medium heat, melt butter and oil, then add shallots until fragrant. Add shiitakes and stir until golden. Add milk and thyme, stirring constantly for about 3 minutes until combined and thickened. Add pinch of salt, then reduce heat to simmer and remove thyme. Squeeze half of a lemon into sauce.
Add pasta into sauce, stirring until fully covered.
Next, sauté your oyster mushrooms in some melted butter, stirring constantly until crispy, but not burnt. Add to pasta with parmesan as a crunchy topping.