Split breast: Cut each breast in half horizontally to form 4 thin steaks in total.
Dust with flour: Sprinkle each side with salt and pepper, then sprinkle with flour and use your fingers to spread it all over the surface.
Cook chicken: Melt 15g butter in a large non-stick frying pan over medium-high heat. Add chicken and cook each side for 2 1/2 minutes until golden brown and just cooked through. Remove from pan, cover, and keep warm.
Cook mushrooms: In the same frying pan, add remaining butter and increase heat to high. Add mushrooms and cook for 4 minutes, until starting to turn golden brown on the edges.
Add garlic: Then add garlic and a pinch of salt and pepper and continue cooking for another minute until both garlic and mushrooms are golden.
Deglaze skillet: Add white wine – it will bubble and be steamy! Cook for 30 seconds, scraping the bottom of the pan, until wine is mostly evaporated, and the alcohol smell is gone.
Make creamy sauce: Add chicken stock, cook vigorously for 1 minute so it mostly evaporates. Then add cream, lower heat to medium and simmer for 2 minutes until it reduces and thickens slightly.
Add parmesan: Stir in parmesan, taste, and adjust salt and pepper if needed.
Finish chicken in sauce: Return chicken to sauce for 30 seconds, warm through slightly. Garnish with chives and serve as-is in the pan, for people to help themselves (or transfer to a serving platter, if preferred).