Mix the yeast and a tablespoon of maple syrup with 1 cup lukewarm water in a large bowl. Mix and then add to it 1 cup bread flour. Mix with with a wooden ladle for a minute. This is the starter. (See notes below if using active dry yeast.*)
Cover the starter with a tight lid or cling wrap and set aside in a warm spot overnight or for at least six hours. The starter will get puffy initially and will then settle down and will look very bubbly.
Mix the ½ cup of milk with ¼ cup of water and heat until lukewarm. Add to the bubbly starter along with maple syrup and olive oil.
Next stir in a tablespoon of caraway seeds, a cup of rye flour, 1 ½ cups of bread flour and salt into the starter. Use a wooden spoon to vigorously mix the flours into the starter until a shaggy dough forms.
Turn out the dough onto a well-floured surface and begin kneading it, adding more bread flour as necessary, until very smooth and supple but still very slightly tacky--it should not stick to the surface when kneading. I needed almost ½ cup more of bread flour. Form a smooth ball with the dough.
Oil the bowl you made the dough in and place the ball of dough in it. Coat the top of the dough with oil, then cover the bowl with a tight lid or cling wrap and place the dough in a warm spot until it has doubled, about 1 to 1½ hours.
After the dough has doubled, turn it out on a surface, making sure that the top of the dough ball is now on the bottom. Punch the dough down into a disc.
Roll up the dough into a cylinder. Press in the seams and tuck in the ends to form a loaf. Make sure that the loaf is seam side down when you place it in an oiled loaf pan.
Brush the top of the loaf with a mixture of 1 teaspoon maple syrup and 1 teaspoon non-dairy milk, if you wish, for a better color to the baked loaf. Sprinkle the top with optional caraway seeds.
Cover the loaf with a clean shower cap or with a kitchen towel. Set aside in a warm spot to rise for 1 ½ hours or until the dough has domed nicely over the top of the loaf pan.
In the half hour before the loaf has finished rising, preheat the oven to 450 degrees Fahrenheit/230 degrees Celsius.
Place the loaf pan in the preheated oven and immediately turn the temperature down to 400 degrees Fahrenheit/205 degrees Celsius. Bake 45 minutes.
Let the baked bread stand on a wire rack for 20 minutes or until the loaf pan is cool enough to handle. The loaf should easily pop out of the pan. Return the loaf to the cooling rack until it has cooled to room temperature. Slice and serve.