Place 1 teaspoon bouillon paste and 1 teaspoon gochujang in each of three 1½-pint canning jars. Layer ½ cup cabbage, ½ cup mushrooms, ¼ cup kimchi, 3 ounces shrimp and ½ cup noodles in each jar. Top each with some radish slices, 1 teaspoon cilantro and 1 lime slice. Cover and refrigerate for up to 3 days.
To prepare one jar of noodles: Add 1 cup very hot water to a jar. Cover and shake to combine. Uncover and microwave on High in 1-minute increments until steaming hot, 2 to 3 minutes total. Let stand 5 minutes. Stir before eating.
To make ahead: Prepare through Step 1. Refrigerate covered jars for up to 3 days.