In a medium saucepan, bring the milk, half the onions and the nutmeg to a simmer over medium. Remove from the heat; let stand 15 minutes. Strain; return the milk to the pan, discarding solids in the strainer. Heat over medium; add the flour and whisk until thickened, 5 to 6 minutes. Season sauce with salt and pepper.
Meanwhile, in a large nonstick skillet, cook the bacon over medium until crispy, 8 to 9 minutes. Drain on paper towels; chop. Pour off all but 1 tbsp. of drippings.
Preheat the oven to 350 degrees . Heat the skillet with drippings over medium-high. Add remaining onion and the garlic; stir until soft, 2 to 3 minutes. Add the mixed vegetables, chicken and bacon; stir 1 to 2 minutes. Add to the sauce. Divide among four 8-oz. ramekins.
Place 1 sheet of phyllo on a cutting board; coat with cooking spray. Fold the sheet in half, coat again, then fold in half. Set on one of the ramekins; coat again. Place on a baking sheet. Repeat with remaining phyllo and ramekins.
Bake until the tops are golden and the filling bubbles, 20 to 22 minutes.