In the bowl of your stand mixer mix vanilla pudding according to package directions.
In a small bowl combine warm water, yeast, and sugar. Cover and proof for 7 min until foamy.
Add melted butter, beaten eggs, and salt to pudding and mix with dough hook. While mixing add yeast mixture and combine.
Add flour gradually, 2-3 cups at a time, mixing well between each addition, until dough comes together. Do not overflour dough. Once dough has cleared the sides of the bowl and is still a bit sticky knead for 7 min. If dough is still not coming together and is too sticky, add a bit more flour and knead until a supple, smooth, tacky dough forms.
Place dough in lightly oiled bowl, cover, and rise until doubled.
For the filling combine all ingredients in a large bowl.
Once dough has risen, butter a 9x13 and a 9 in pan. Empty dough unto work surface and roll and pat into an 20x28 in rectangle about 1/2 in thick. Spread filling evenly over the top. Starting at the long end, roll dough up, not too tightly otherwise the centers will pop out. Pinch seams together and flip log seam side down. Slice rolls about 1 1/2 in thick. Place rolls in buttered dish, seams together and touching.
Let rolls rise for 30-45 min until puffy but not doubled in size. Place rack in lower part of oven. Preheat oven to 375℉. Bake for 20-30 min until golden.
For the frosting, melt butter in saucepan over medium heat until it sizzles. Swirl butter and cook until golden and fragrant. Remove and cool. Combine 1/4 cup boiling water and 2 Tbsp loose leaf Earl Grey tea and steep for 10 min. All the water will absorb.
In a stand mixer bowl fitted with whisk attachment beat softened cream cheese and powdered sugar until smooth, scraping down the sides of the bowl. Add cooled browned butter, vanilla, salt, steeped tea leaves, and nutmeg. Whip until fluffy.
Frost rolls while slightly warm so frosting melts into cracks and creates a gooey roll.