Preheat oven to 350°F (175°C) and line a baking sheet with parchment or a silicone mat.
In a small saucepan over medium heat, melt the butter and stir in the brown sugar and corn syrup for 1–2 minutes until the mixture is smooth.
Remove from heat and whisk in the vanilla, flour, and salt until combined.
Stir in the chopped nuts (or oats) until they are fully coated; the batter should be thin and pourable.
Use a teaspoon to drop small rounded mounds (about 1 tablespoon each) onto the prepared sheet, spacing them at least 2 inches apart.
Baking
Bake for 6–9 minutes, rotating the pan halfway, until edges are deeply golden and centers are lacy.
Let cookies cool on the sheet for 1–2 minutes to firm, then transfer to a wire rack to cool completely.
Shape into cones if desired while warm, using a rolling pin or small jar.
Notes
Store in an airtight container layered with parchment for up to 5 days. Freeze in a single layer for up to 8 weeks. Re-crisp softened cookies in a 300°F (150°C) oven for 3–5 minutes.