Preheat oven to 350 degrees. Gently wash, hull, and cut strawberries into quarters. Place berries on a cooling rack over a sheet pan. Bake until strawberries are partially dried, about 45 minutes. Let cool.
Increase oven to 400 degrees. Brush a 12-mold muffin tin with 2 tablespoons melted butter. Set aside.
In a bowl, whisk together ricotta, eggs, and vanilla. Stir in remaining butter.
In a large bowl, use your fingertips to rub together sugar and lime zest until sugar is moist. Mix in flour, baking powder, salt, and baking soda. Use a spatula to gently but quickly fold ricotta mixture into dry ingredients. Don’t overwork it. The batter will be thick and heavy. Stir in strawberries and spoon batter evenly into muffin tins. Bake until tops of muffins are golden and springy to the touch, about 20-25 minutes.