The phrase "thickest portion" refers to the part of something that is the largest or has the most amount of material. It is the thickest part of an object. Full definition
To make the frosting: Use the top, thick portion of the chilled coconut cream and put in a small mixing bowl. (onedegreeorganics.com)
Turn chicken; grill, covered, until a thermometer inserted in thickest portion of thigh registers 160 °F. (myrecipes.com)
Smoke the pork, maintaining temperature inside smoker at 225 °F, until pork is tender and a meat thermometer inserted into thickest portion registers at least 145 °F, about 4 hours. (chowhound.com)