Heat a medium saute pan over medium-high heat. Add the oil and spread around pan. Add the onion and saute until soft. Add the cooked barley and garlic to the pan. Pour in 1/2 cup of the chicken stock, stirring continuously. Once all the liquid is absorbed, add in 1/2 cup of the white wine, stirring continuously until all the liquid is absorbed. Continue the same process, adding 1/2 cup of chicken stock followed by 1/2 cup of wine, until 1/2 cup of chicken stock remains. Add the mushrooms, asparagus, tomatoes and thyme. Cook until the vegetables have softened, then add the last 1/2 cup of chicken stock. Once all the liquid is absorbed, add the Parmesan cheese, half-and-half, salt and pepper. Reduce heat to low and stir to combine.