Prepare the Slow Cooker: Set your slow cooker to the low heat setting.
Sear the Meat: In a large skillet, heat the olive oil over medium-high heat. Add the chopped onions and garlic; sauté for 2-3 minutes until translucent. Add the beef stew meat and brown on all sides, about 5 minutes. Stir in the paprika and caraway seeds; cook for an additional minute.
Combine Ingredients in Slow Cooker: Transfer the seared meat and onion mixture to the slow cooker. Add the diced red and green bell peppers, diced tomatoes, and bay leaf. Pour in the beef broth. Season with salt and pepper and stir.
Cook the Goulash: Cover the slow cooker and cook on low for 4-6 hours, or until the meat is tender and the flavors meld together.
Make Cucumber Water: In a pitcher, combine the cucumber and water. Refrigerate to chill, and add ice cubes just before serving.
Prepare the Bread: Toast the slices of crusty bread and spread with butter.
Prepare the Ice Cream Milkshake: In a blender, combine vanilla ice cream, milk, and chocolate syrup. Blend until smooth and creamy.
Serve: Once the goulash is ready, remove the bay leaf. Serve the Hungarian goulash in bowls with toasted bread on the side, cucumber water, and milkshake. Optionally, top the milkshake with whipped cream and a maraschino cherry.