Bring a large pot of salted water to a boil and fill a bowl with ice and water.
Add the asparagus to the boiling water and blanch until tender, 3 to 4 minutes, depending on the size. The asparagus are done when you can put the tip of a paring knife into a spear and it's tender throughout.
Immediately plunge the asparagus spears into the ice water to stop the cooking and preserve their color. Once the asparagus are cool, set on a clean kitchen towel to drain. Set aside.
Heat the olive oil and r tablespoon of the butter in a small sauté pan over medium heat. Add the morels and 120 ml water and season with salt and pepper. Cover and simmer for 2 to 3 minutes. Add another tablespoon butter and cook, uncovered and stirring occasion ally, until the morels are tender and the liquid has evaporated, 2 to 3 minutes. Season with salt and pepper and keep warm.
In a medium sauté pan, melt the remaining tablespoon butter over medium heat. Add the asparagus and sauté until the spears are warmed through and the butter is nutty brown, 3 to 5 minutes, depending on the size. Season with salt and pepper and keep warm.