In a medium bowl, toss the peaches with lemon juice. Add the brown sugar and cinnamon and stir to combine. Let stand 30 minutes.
Drain the peaches well and toss with flour. Reserve 1/4 cup of peaches for the muffin tops.
In a medium bowl, whisk together the flour, sugar, brown sugar, cinnamon and salt.
With a pastry blender, or with your fingertips, work the butter into the flour mixture until it looks like wet sand. Press together to form chunks. Set aside in the refrigerator until ready to use.
Preheat the oven to 375ºF (190ºC). Line a 12-serving muffin pan with tulip muffin liners.* (Tulip muffin liners are preferable because they hold more batter, but you can also use standard muffin liners.)
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon and nutmeg.
In a large bowl, beat the butter and sugar together until light and fluffy. Beat in the eggs and extracts in 3 separate additions, making sure each one is incorporated before adding the next.
Mix in the flour mixture with a wooden spoon or spatula, in two additions, followed by half of the sour cream after each addition. Mix just until combined. The batter will be thick.
Toss the white chocolate chips with flour, then fold them into the batter. Gently fold in the drained peaches.
Transfer batter to the prepared muffin pan, equally dividing the batter among the muffin cups. (If you’re using standard muffin liners, fill them 2/3 full.) Top with the reserved peaches and the crumb topping. Optional: Top each muffin with a piece of white chocolate.
Bake muffins for 5 minutes. Turn down the oven heat to 350ºF (180ºC). Continue baking until the muffins are light golden brown and a toothpick inserted into the centers of the muffins comes out clean, about 15-20 more minutes. Cool in the pan for 5 minutes, then remove the muffins from the pan and continue cooling on a cooling rack.