Preheat the oven to 400°F.
In a large pot, bring the water, milk, butter and salt to a boil. Reduce heat to low and whisk in the polenta. Cook, stirring regularly, for 20 minutes. Fold the cheese into the polenta and cook for 10 more minutes. Season with salt and pepper.
To make the sofrito, heat a medium skillet over medium heat with the olive oil and butter. When the butter melts, add the onion, garlic, celery and thyme and cook, stirring, until softened, about 5-7 minutes. Add the ham, bell pepper and jalapeño and cook for 10-15 minutes, stirring regularly. Season with salt and pepper.
In a small saucepan, heat the tomato paste and vegetable stock, stirring until the paste is dissolved.
Place the tomatoes on a baking sheet, toss with olive oil, thyme, salt and pepper and roast for 8-10 minutes, until starting to soften.
Combine the seasoning for the shrimp in a large bowl, add the shrimp, oil and a pinch of salt and pepper and toss to coat. Transfer to a baking sheet and roast for 5-8 minutes, stirring once, until pink and cooked through.
To serve, divide the poletna between plates. Top with sofrito, roasted tomatoes, and shrimp and drizzle with tomato jus.