Heat small saucepan over medium-low heat. Once pan is warm, add butter. Let butter melt completely, then sprinkle all-purpose flour into saucepan. Whisk until butter and flour are fully combined and thick paste-like mixture forms.
Whisk constantly to prevent burning and continue heating roux over medium-low heat until golden brown in color, approximately 5-10 minutes.
Once desired color is achieved, add curry powder, garam masala, and cayenne pepper to roux. Whisk to incorporate spices, then cook mixture 30 seconds. Remove saucepan from heat and use mixture immediately, or transfer to airtight container and let cool completely. Once cooled, seal container and refrigerate mixture until ready to use.
For the Curry Fries
Preheat oven to temperature on frozen french fry packaging. Once preheated, cook fries according to packaging instructions.
While fries cook, heat medium saucepan over low heat. Once saucepan is warm, add 4 tablespoons of curry roux mixture and 3 cups chicken stock. Whisk until ingredients are well combined.
Increase heat under saucepan to medium-high. Bring mixture to boil, then reduce heat to medium-low and let mixture simmer 5 minutes or until thickened.
Once mixture has thickened, remove saucepan from heat. Add room temperature shredded cheese to saucepan and whisk well to incorporate.
When fries are ready, portion fries into serving dishes. Top fries with one over-easy egg per dish. Pour curry sauce over egg and fries, then sprinkle sliced green onions over top of dish. Garnish with halved grape tomatoes, black sesame seeds, and togarashi if desired, then serve immediately.