For the tomato dip, drain the tomatoes and cut them into small pieces. Wash basil, shake dry, pluck off leaves and chop finely. Mix tomatoes, tomato paste, basil, 1 teaspoon sour cream and stock. Season to taste with salt and pepper. Set aside covered.
For the avocado dip, peel the garlic and chop very finely. Wash lime hot, grate dry, finely grate peel, cut lime in half and squeeze juice from one half, cut second half into slices. Cut avocado in half along the core, remove core and skin. Cut half of the avocado into fine cubes, finely puree the remaining avocado with garlic, sugar, 50 g sour cream, lime juice and zest. Stir in the avocado cubes and set aside covered.
Wash the parsley, shake dry, pluck off the leaves and, except for a few for garnishing, chop. Grate cheese finely. Mix Panko with cheese and chopped parsley. Whisk eggs, season with salt and pepper. Put flour in a bowl, turn tortelloni in several portions first in flour, then in whisked egg and panko mixture. Heat the oil in a wide pan and fry the tortelloni in it in 2-3 portions until golden brown. Drain on kitchen paper. Arrange tortelloni with dips. Garnish with parsley and add lime wedges.