In a stand mixer fitted with paddle attachment, cream together butter, brown sugar, granulated sugar, egg, and vanilla on medium-high speed for about 4 minutes until fluffy.
Scrape down sides of bowl, add cream or half-and-half, and mix on low speed until combined, about 1 minute.
Add flour, pumpkin pie spice, corn starch, baking soda, and optional salt. Mix on low speed just until incorporated, about 1 minute.
Add pecan halves and mix on low speed for 30 seconds just to combine.
Using a 1/4-cup measure or large cookie scoop, form 14 equal dough mounds. Roll into balls and flatten slightly.
Place dough balls on a plate and cover with plastic wrap. Refrigerate for at least 3 hours or up to 5 days. Do not bake unchilled dough to avoid spreading too much.
Preheat oven to 350°F. Line baking sheets with silicone mats or grease them lightly. Space cookies at least 2 inches apart, baking about 8 per sheet.
Bake for 10 minutes until edges are set and tops appear just set but still slightly glossy in the center. Avoid overbaking.
Allow cookies to cool on the baking sheet for 10 minutes before serving. Do not transfer immediately to racks.
Notes
These cookies are buttery and perfectly spiced, with crunchy pecans in every bite. Chill dough well to reduce spreading and get thick, soft cookies.