In a large bowl, cream butter and sugars until light and fluffy. Add eggs, one at a time, beating well after each addition. Combine the flour, baking soda and salt; gradually add to creamed mixture and mix well (dough will be sticky).
For filling, combine the rhubarb, sugar and 2 tablespoons water in a large saucepan. bring to a boil. Reduce heat; simmer, uncovered, for 10 minutes or until thickened, stirring frequently. Combine cornstarch and remaining water until smooth; stir into rhubarb mixture. Bring to a boil; cook and stir for 2 minutes or until thickened. Remove from the heat; stir in vanilla.
Drop dough by tablespoonfuls 2 in. apart onto ungreased baking sheets. Using the end of a wooden spoon handle, make an indentation in the center of each cookie; fill with a rounded teaspoon of filling. Top with 1/2 teaspoon of dough, allowing some filling to show. Bake at 375° for 8-10 minutes or until lightly browned. Yield: about 4-1/2 dozen.