Heat a large skillet over medium-high heat. Add the oil and then stir in the onions. Cook for about 2 minutes or until the onions are soft.
Add the carrots and cook for about 3 minutes, stirring occasionally. Add the garlic and celery, and continue cooking until the celery and carrots are tender, 3 to 5 minutes.
Stir in the lemon juice and thyme. Remove from heat and toss with the Parmigiano-Reggiano.
Season with salt and pepper and serve warm.
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