Line an 8x4 inch loaf pan with parchment paper, ensuring some overhang for easy removal.
In a small heavy-bottomed saucepan, combine the pumpkin puree, honey (or maple syrup), and pumpkin pie spice.
Simmer the mixture over medium-low heat for 25 to 30 minutes, stirring frequently with a silicone spatula to prevent sticking.
Continue cooking until the moisture has evaporated and the mixture is very thick, resembling the consistency of dense mashed potatoes.
Remove the pan from the heat and immediately whisk in the coconut oil and vanilla extract until the mixture is completely smooth and glossy.
For an extra smooth texture, process the mixture with an immersion blender for 30 seconds.
Pour the pumpkin caramel into the prepared loaf pan and smooth the surface with a spatula.
Sprinkle the top evenly with flaky sea salt.
Refrigerate the pan for at least 2 hours until the caramel has set firm.
Lift the parchment paper out of the pan and slice the block into 16 even squares using a sharp, warm knife.
Store caramels in an airtight container in the refrigerator to maintain their firm, chewy texture.