Preheat the oven to 375 degrees F.
Place the pine nuts and pumpkin seeds on a sheet pan and place in the oven. Roast the nuts until golden, shaking the pan periodically to ensure even browning, about 10 minutes.
Line a large sheet pan with a silpat cover, or, with aluminum foil. Smooth out any wrinkles that form on the sheet pan, grease with the vegetable oil and set aside. In a large, heavy-bottomed saucepan, combine the sugar and water and bring to a boil, without stirring. Add the corn syrup and continue to boil the sugar, brushing down the sides of the saucepan with a brush that's been dipped in water to force down into the pan any crystallized sugar that forms on the walls of the pan.
When the sugar reaches 250 degrees F, gradually add the butter, but do not stir. Continue to cook the sugar until it starts to turn a light caramel color. Remove from the heat and add the salt and baking soda, stirring to distribute. Pour the sugar over the silpat and cover evenly, making a thin sheet over the silpat. While the sugar is still warm, sprinkle the pine nuts and pumpkin seeds over the candy. Allow to cool completely before breaking and serving.