In a small bowl, mix yeast, lukewarm whole milk and sugar. Stir and wait for yeast to bloom 10 minutes. Sift flour and salt into mixing stand bowl. Add dried basil and rosemary. Stir to combine thoroughly.
Add yeast mixture and eggs to dry ingredients, use dough hook to mix for 2 mins until well combined. Increase speed to medium until a dough is formed approx 4-5 mins. Scrape down sides. Knead for another 3 minutes until dough becomes soft and smooth.
Lower speed and gradually add in butter, 2 Tbs at a time until it is well mixed. Dough should be very soft when done, about 4-5 minutes. Gently form dough into a ball and put into a well oiled large container. Cover and let the dough rest at room temperature till double in size, approx 60 mins.
Remove from container and punch down dough. Shape into a rough rectangle, wrap tightly with cling wrap and chill for an hour.
When dough is chilling, prepare the filling. In a small bowl, stir together pesto and ricotta cheese. If using, squeeze out roasted garlic into a bowl. Mash lightly. Mix well. Taste and adjust filling to suit. Next, line the round pan with parchment paper.
Unwrap chilled dough onto a lightly floured work surface. Roll out into a rectangle, approx. 14” x 20” (36 x 50cm). Spread the filling evenly all over the rectangle, leaving approx. half an inch (1-2 cm) around the border. Gently but firmly roll up the rectangle on the long side.
Cut the roll in half, lengthwise approx 1-2” (3-5 cm) on one end, exposing the filling, creating 2 long pieces of dough. Gently criss-cross the dough pieces, and tucking the ends together to create a wreath.
Transfer shaped wreath into prepared parchment lined 9” (23cm) round pan and cover with cling wrap. Let rise at room temperature for 30 minutes. When waiting, preheat oven to 350°F (175°C).
Brush egg wash over the brioche. Pop into the oven for 40-50 mins, or until the bread is golden brown, or when the internal temperature reads 190°F (88°C).