Pat chicken cutlets dry and season both sides with kosher salt and black pepper.

Add the flour to a large plate or shallow bowl and dredge each cutlet, shaking off any excess.

Heat the olive oil in a large skillet over medium heat. Once shimmering, add the butter. It should foam straight away. If it just sits there, the pan is not hot enough yet.

As soon as the butter melts, add the chicken cutlets in a single layer. Do not crowd the pan; work in two batches if they do not all fit with space between them.

Cook until golden brown on the first side, about 5 minutes.

Flip and cook the second side until golden and cooked through, about 4 to 5 minutes.

Transfer the chicken to a plate or sheet pan and set aside.

Pour off the excess fat, leaving about 1 to 2 tablespoons in the skillet. Do not wipe it out.

Return heat to medium (lower than searing). Add the tomato paste and cook 2 minutes until it deepens in color. Add the chopped garlic and cook 30 to 60 seconds until fragrant. You'll know you're ready to move on when the paste loses its raw smell and starts to stick to the pan. Those browned bits are flavor, and you get them all back the moment you deglaze.

Stir in the oregano and red pepper flakes to taste.

Pour in the chicken stock.

Bring to a simmer and scrape up the browned bits from the bottom of the pan.

Let the stock reduce by half, about 5 minutes.

Add ½ cup heavy cream and stir. Let the sauce simmer gently until slightly thickened, about 3 minutes. You're looking for a bare simmer: small bubbles breaking the surface, not a rolling boil.

Add the grated parmesan and sun-dried tomatoes. Stir to melt the cheese into the sauce.

Taste and adjust with salt and pepper. Add more cream if you want a richer sauce.

Return the chicken cutlets to the pan and simmer in the sauce for 3 to 4 minutes until warmed through.

Remove from heat, garnish with fresh basil, and spoon sauce over each serving.