Bring a large pot of salted water to a boil. Cook the pasta until it reaches al dente, according to the package directions.
Heat 1 tablespoon of the oil in a large skillet over medium heat. Sprinkle the chicken on both sides with salt and pepper. Sear the chicken, covered, for 5 minutes. Flip and sear another 5 minutes, covered. Remove the chicken from the pan and set aside to rest. After a few minutes, give the chicken a good chop.
Back in the skillet, add the remaining tablespoon oil. Add the carrots and cook, stirring, until they start to soften, about 4 minutes. Add the onions and asparagus and cook, stirring, until the asparagus is crisp-tender, another few minutes. Add the garlic and cook, stirring, until it becomes fragrant, about 30 seconds. Season the veggies with a pinch of salt and pepper and reduce the heat the low.
In the meantime, melt the butter in a small saucepan. Once the foaming subsides, add the flour and whisk until the color changes from cream to a golden brown, just a few minutes. Slowly add the milk, continuing to whisk over medium heat, until it becomes a bit thicker and creamier. Now, add the Parmesan and a good pinch of salt. Keep whisking until the cheese is melted and the sauce is good and creamy. Taste it and add more salt if needed.
Ladle out about 2/3 cup cream sauce and add it to 1 cup cooked pasta, tossing to coat. Divide between 2 kids' plates and top with chopped chicken and extra Parmesan. Done! (Feel free to sprinkle the veggies on the kids' plates, if they'll remotely let you.)
Now, back to the cream sauce: stir in the vodka and let it simmer for a couple of minutes.
For your adult plates, serve the creamy pasta with chicken and a good helping of cooked veggies. Garnish with extra Parmesan and fresh parsley.