In a large skillet over medium-high heat, warm a drizzle of olive oil until shimmering. Add the boneless, skinless chicken breasts, cooking for about 10 minutes, turning halfway, until golden brown and cooked through.

In the same skillet, add more olive oil if needed, and toss in the finely chopped yellow onion and minced garlic. Sauté for about 3 minutes until the onion is translucent and the garlic is fragrant.

Stir in the fresh broccoli florets and grated carrots, blending them with the sautéed onion and garlic for about 2 minutes. Then, pour in the chicken broth, followed by the dry orzo and spices. Stir everything well.

Cover the skillet, reduce the heat to medium, and let the mixture simmer for 6 minutes. After this time, uncover and give it a gentle stir, cooking for an additional 2 minutes.

Lower the heat and pour in the milk, stirring to combine with the orzo mixture. Add the freshly grated cheddar and parmesan cheeses and gently mix until melted and creamy.

Taste for seasoning and adjust as necessary. Serve immediately while warm, garnished with extra cheese or fresh herbs if desired.