Line the bottom and sides of an 8” x 8” square metal or glass pan, and lightly butter the foil.
In a medium saucepan, combine the sugar, corn syrup and water. Cook over medium-low heat, stirring constantly, until the sugar is completely dissolved.
Raise heat to medium-high, and bring to a simmer. Allow to remain at a vigorous simmer, without stirring, until the mixture turns a medium amber color, approximately 15 minutes.
Remove the pan from the heat, and add the cream, butter, and salt. The mixture will bubble wildly, but stir slowly with a heat-resistant rubber spatula, or a wooden spoon, until completely blended and smooth. Stir in the vanilla extract.
Pour the caramel into the prepared pan, and allow to set at room temperature, about 1 hour.
Remove from the pan, peel away the foil, and cut into desired uses.
Salted Caramel: immediately after pouring hot caramel into the pan, sprinkle the surface of the caramel with flaky sea salt. Allow to set, then cut into small, ¾” squares or rectangles.
Caramel-on-a-Stick: Once the 8 x 8 block of caramel is set, cut into 8 equal rectangles, 2” x 4”. Cut each rectangle across the diagonal, into 2 right triangles. Insert a lollipop stick into the bottom end of each triangle. Optional: Dip the triangles in melted dark chocolate.
Nutty Little Caramel Logs: Before pouring hot caramel into the prepared pan, stir in 1 cup of chopped pecans or cashews, then pour into pan. Once set, cut caramel into ¾” wide strips, then into 1” long pieces. Roll each piece into a log. Wrap each log in clear cellophane and twist the ends.
Big Caramel Logs: Pour the plain hot caramel into the prepared pan, and allow to set ½ hour. Cut it in half, and roll each half into a thick log. Roll the log in chopped pecans or cashews, pressing the nuts into the surface of the caramel log. Allow to set until completely cool, and firm. To serve, slice the log crosswise, into round discs of caramel, framed by chopped nuts.