In a skillet, heat 3 Tbsp. olive oil over medium high heat. When the oil is hot, add the sliced mushrooms and saute until golden brown, 5-6 minutes. Season with a little salt and pepper and then set aside to cool.
In a large serving bowl, whisk the remaining 4 Tbsp. olive oil with the lemon juice. Adjust seasonings to taste. Add the celery, radishes, cooled mushrooms, Parmesan cheese, and parsley to the bowl and toss until combined. Season with sea salt and pepper.