In a large skillet, heat the butter and olive oil over medium-low heat. Throw in the onions, garlic and thyme and cook, stirring occasionally, until the onions are golden brown and soft, 20 to 25 minutes. Stir in the brown sugar until melted. Continue cooking until very deep in color, 5 to 7 minutes more. Remove from the heat and let cool completely, about 20 minutes.
In the bowl of a food processor, add the ricotta and sour cream and process until smooth. Season with salt and pepper, then add the chives, Worcestershire, 2 tablespoons of the parsley and three-quarters of the caramelized onions, reserving the rest for garnish. Pulse 5 or 6 times, until the onions are incorporated but still have some texture. Taste and adjust the seasoning as needed.
Transfer the dip to a serving bowl. Top with the reserved caramelized onions and sprinkle over the remaining parsley. Serve with chips, carrots, radishes and sugar snap peas.