Boil baby carrots in salted water until just tender. Do not over cook. Remove from heat, drain and set aside.
In a large skillet or saute pan, heat the olive oil and butter over medium-high heat. Add the shallots and garlic and cook until the shallots are translucent. Add the mushrooms and cook until they begin to become tender and release their juices. Let cook for a few minutes to allow flavors to blend. Deglaze the pan with the white wine and add the pattypan squash. reduce heat to low, cover and let cook until squash becomes tender but not mushy (about 15 minutes). Remove cover and increase heat back up to medium or medium-high and allow most of wine to evaporate. When most of the wine is gone, stir in the Brussels sprouts and carrots and gently stir to coat with the remaining pan juices. Remove from heat and stir in hoisin sauce.