Preheat the oven to 350°F (175°C). Spread the measured flour evenly on a rimmed 18x13-inch baking sheet and bake for 5 minutes to toast and heat-treat the flour; remove and let it cool completely.
In the bowl of an electric mixer fitted with the paddle attachment, cream together the softened butter, packed light brown sugar, granulated sugar, and salt on medium speed until the mixture is pale and fluffy, about 3 minutes.
Add 1 1/2 tablespoons half-and-half and the vanilla extract to the creamed butter and mix until combined.
Add the cooled toasted flour and mix on low speed just until the dough comes together; do not overmix.
If the dough seems dry, add additional half-and-half 1/2 tablespoon at a time until it holds together and can be scooped.
Stir in the chocolate chips, reserving a few if you want to press them onto the tops of the formed bites.
Scoop about 1 tablespoon of dough at a time and roll into balls. Place the bites on parchment paper and press reserved chips onto the tops if desired.
Serve immediately or store the cookie dough bites in an airtight container in the refrigerator.