Combine the flour, salt, pepper and about 1 1/2 tsp. dried oregano. Stir to mix well.
Gently roast the cherry tomatoes on a sheet pan lined with foil. Drizzle the tomatoes with olive oil and salt. Preheat oven to 400 degrees and roast for about 10 minutes until the tomatoes just begin to pop. Set aside.
Pound the chicken breasts to an even 3/4 to 1 inch thickness. Place the chicken breasts and flour dredging mixture in a large zip lock bag and toss and roll around until all sides of the chicken are coated thickly and evenly.
Heat the olive oil and butter in a large, heavy bottomed skillet over medium-high heat. Shake the chicken breasts slightly and gently drop in the hot oil/butter. Brown for about 3 minutes on each side until golden brown. Transfer to a tray or platter.
Turn the heat down to medium and add the chopped garlic. Stir for about 1 minute until you can smell the garlic. You do not want it to brown. Add the chicken broth/wine to deglaze the pan and stir to bring up any brown bits from the chicken that may have stuck to the bottom of the pan. Cook this down for 10-15 minutes to cook off the wine.
Stir in the cream, basil, oregano, and Parmesan. Bring to a simmer and cook stirring frequently until the sauce slightly thickens; about another 10-15 minutes more.
Stir in the spinach and blistered cherry tomatoes. Next add the chicken back into the pan making sure they are well covered with sauce and veg. Cook for another 5-10 minutes until chicken registers 165 degrees doneness.
Serve with your choice: pasta, risotto, potatoes or simply salad and bread sticks. Sprinkle with parsley and parmesan and one pretty piece of basil.