Combine vegetable broth and lemon juice in a large pot, bring to a boil, and cook kohlrabi until softened, about 20 minutes. Drain broth and reserve. Allow kohlrabi to cool lightly and scoop out the insides. Set aside kohlrabi shell and kohlrabi flesh.
Meanwhile, bring a large pot of lightly salted water to a boil. Cut a small "x" into each tomato and boil for 1 minute. Drain tomatoes, remove tomato skins and seeds, and finely chop.
Melt butter in a skillet over medium-low heat and cook shallots until soft and translucent, about 5 minutes.
Preheat the oven to 400 degrees F (200 degrees C). Grease a baking dish.
Finely chop kohlrabi leaves. Combine sauteed shallots, kohlrabi leaves, 1/2 of the tomatoes, feta cheese, green onions, parsley, garlic, and pepper in a bowl; mix to combine. Fill kohlrabi shells with the mixture.
Set stuffed kohlrabi close together in the prepared baking dish and sprinkle kohlrabi flesh and remaining tomatoes in between. Pour 1 cup of kohlrabi cooking water into the dish.
Bake in the preheated oven until kohlrabi is soft and filling is lightly browned and cooked through, 20 to 30 minutes.