Combine milk, water, oil, bay leaves, salt and pepper to taste in large pot over high heat. Bring almost to boil.
Add polenta while stirring, and cook, stirring constantly, until thick, about 6 minutes. Remove from heat and add butter, stirring, 1 tablespoon at a time. Stir in cheese and thyme.
Transfer to 2-inch-deep baking dish and set aside to cool and solidify, about 30 minutes.
While polenta is cooling, soak chorizo in cold water, 5 minutes, to prevent casings from cracking. Cook in grill pan over low heat 30 to 40 minutes.
Heat cast-iron grill pan or charcoal grill over medium-high. Brush tomatoes with oil and place in pan, cut sides down. Cook until heat through, with grill marks, about 8 minutes.
Slice polenta and grill until heated through and grill marks appear. Top with tomatoes and chorizo and serve with chimichurri on the side.