Position the racks in the middle and lower third of the oven. Preheat the oven to 350 degrees Fahrenheit. Line 3 large cookie sheets with parchment paper.

Into a large bowl, sift together the flour, baking soda, and salt.

In the bowl of a standing electric mixer, cream the butter with both sugars on medium speed until light and fluffy. Add the whole egg and egg yolk and beat until blended. Beat in the vanilla. Gradually add the dry ingredients, and then the chips and cherries, blending until just incorporated.

Using a medium cookie scoop or a soup spoon, drop the dough onto the lined cookie sheets., leaving 1 ½ inches between the mounds. With your fingers, flatten each cookie ½ inch thick.

Bake the cookies for 15 minutes, or until golden, rotating the sheets halfway through the baking time and turning them front to back, as well. (If all 3 sheets will not fit in the oven at the same time, hold 1 in the refrigerator until the first batch of cookies is removed.) Cool the cookies on the sheets, set on racks. Store in an airtight container.