Line a 9x13-inch baking dish with parchment paper (or grease well) and set aside. Chop the rosemary and thyme. In a small bowl, mix the Greek yogurt, olive oil, minced garlic, lemon juice, and salt; refrigerate until serving.
In a medium saucepan, bring the chicken stock and water (4 cups total) to a boil. Add the sea salt, then slowly whisk in the polenta in a steady stream to prevent lumps.
Reduce heat to low and cook, stirring constantly, until thick and smooth, about 5–10 minutes (or until the polenta pulls away from the sides). Stir in the Parmesan, olive oil, rosemary, thyme, and black pepper.
Spread the hot polenta evenly in the prepared dish to about 3/4-inch thickness. Cool completely until firm, at least 2 hours (or refrigerate overnight).
Lift out the firm polenta and slice into fries about 3–4 inches long and 1/2 inch thick (or cut into triangles/squares if you prefer).
Bake: Heat the oven to 425°F (220°C). Arrange fries on a parchment-lined baking sheet. Brush all sides lightly with olive oil and bake 30–35 minutes, flipping halfway, until deeply golden and crisp.
Fry (optional): Heat about 2 inches of neutral oil to 375°F (190°C). Fry in batches 3–4 minutes until golden and crisp; drain on a rack or paper towels and season immediately.
Finish hot fries with extra grated Parmesan, flaky sea salt, and more chopped herbs if you like. Serve immediately with the chilled yogurt dipping sauce (or marinara, if preferred).