Warm the bowl of your KitchenAid mixer under the kitchen faucet while using a thermometer to mix the hot/cold water to the right temperature (105°-115°).
In your 2-cup measuring cup combine the 1 cup + 2 tablespoons warm water, 1 teaspoon sugar, and thoroughly dissolve the 2¼ teaspoons yeast in it, set aside.
Meanwhile, sift-measure the flour and add to the bowl along with the salt. Mix well with the standard paddle, replace the paddle with the dough hook.
Add the 1 tablespoon oil to the yeast mixture, (which should have a 'head' of bubbles on it by now, if not discard and start over) and pour the whole thing into the bowl on top of the flour mixture.
Using the dough hook, mix on speed 2 until the dough balls up and cleans the bowl. help it along with a soft spatula if you want. Be patient here, as it will look too dry for the first 5 minutes or so, but will eventually incorporate all the flour and probably need more flour added, so wait at least 5 minutes without adding any liquid.
Knead on speed 2 or 3 for 10 minutes or more, adding flour a tablespoon at a time as necessary to keep too much of the dough from sticking on the bottom of the bowl. Take steps to keep the dough wrapped around the dough hook and getting pulled like taffy, rather than balled-up and rolling around in-between the dough hook and the bowl.
When finished kneading, remove the dough from the bowl, knead by hand a few turns and form into a ball, place in an oiled bowl (1-2 teaspoons oil in the bottom of a bowl) and turn to coat the ball with oil. cover with a towel and place in a warm place (80°-85°) to rise until size-doubled (45 minutes to 1 hour).
When finished rising, dump the dough out of the bowl and knead by hand for 20 turns or so. Form into a loaf, a place in a 9"x5" bread pan. Let rise in a warm place again until it is 1" to 1¼" over the top of the pan (45 minutes to no more than 1 hour) cover loosely with plastic wrap to keep the dough moist. I raise my loaves on top of the stove while it is pre-heating.
Bake in a pre-heated 375° oven for 35 minutes.
Remove from oven and cool pretty-much completely before cutting (if you can wait!).