Trim tops from carrots, if desired. In a large saucepan, cook the carrots 4 minutes in a small amount of boiling lightly salted water. Add the mushrooms. Cover and cook about 4 to 6 minutes more or until the carrots are tender. Drain; place in a large bowl and cool slightly.
In a screw-top jar combine the olive oil, vinegar, snipped dill, salt and pepper. Cover and shake well. Pour over vegetables; toss gently to coat. Cover and chill for 4 to 24 hours.
Allow vegetables to stand at room temperature for 30 minutes before serving. Serve with a slotted spoon. If desired, add red pepper strips. Garnish with fresh dill. Makes 8 to 10 servings.