Pat the chicken breasts dry with paper towels, then lay them between plastic wrap and pound them to an even 1/2-inch thickness—this ensures they cook uniformly and stay tender. In a small bowl, combine the Italian seasoning, red pepper, salt, and pepper. Generously season both sides of each chicken breast with this spice mixture, pressing gently so it adheres well.
Heat the olive oil in a large skillet over medium-high heat until it shimmers. Once hot, carefully place the seasoned chicken breasts in the pan and cook for 5-6 minutes per side until golden brown and cooked through (an instant-read thermometer should read 165°F). Transfer the cooked chicken to a plate and set aside. I like to let the chicken rest briefly on the plate while I make the sauce—it helps keep it juicy.
In the same skillet (don't clean it—those browned bits add flavor), melt the butter over medium heat. Add the diced onion and cook for about 1-2 minutes until it begins to soften, then add the trimmed asparagus pieces. Cook for another 1-2 minutes, stirring occasionally, to start softening the asparagus and allow the vegetables to begin releasing their flavors into the butter.
Add the freshly minced garlic to the pan and cook for about 1 minute, stirring constantly. You want to cook it just until fragrant—this is a critical moment because burnt garlic will taste bitter, so keep the heat at medium and watch carefully. The garlic will perfume the entire dish when timed right.
Pour in the full-fat cream and add the lemon juice, stirring well to combine. Bring the sauce to a gentle simmer over medium heat, then add the grated Parmesan and dried oregano, stirring until the cheese melts completely and the sauce becomes smooth and velvety. Taste the sauce and adjust seasoning as needed—the lemon should be balanced with the richness of the cream, not overpowering.
Gently return the cooked chicken breasts from Step 2 to the pan, nestling them into the creamy sauce with the asparagus and onions. Simmer for 3-4 minutes, allowing the chicken to warm through and absorb some of the sauce flavors. If the sauce seems too thick, add a splash of water or broth to reach your desired consistency. Serve immediately, spooning the creamy sauce and asparagus over each chicken breast.