In a small frying pan, melt 1-1/2 tablespoons butter over medium heat until butter browns and smells nutty, about 2-3 minutes. Set aside to cool.
Blanch peas in boiling water for about 30 seconds. Transfer to a bowl with ice water to cool. Drain the peas and dry well. Transfer the peas to a food processor and purée to a chunky texture. Add the egg, egg yolk, and heavy cream. Purée until just under a smooth texture.
In a medium bowl, add the pea purée and whisk in the flour, brown butter, 1 teaspoon of salt and pepper. Taste for seasoning and adjust if needed.
Heat a large frying pan over high heat, add 1 tablespoon of butter. Melt the butter and then turn heat down to medium. Ladle a tablespoon of batter for each pancake into the pan. Cook for about 4 minutes or until edges turn golden brown and then flip and cook the other side for about 3 minutes. Repeat with the remaining batter, add more butter to pan if needed.