Vectorise Family Café Logo

I need assistance to vectorise an existing logo.

Requirements:
- Vectorise current logo (in JPEG/PNG format)
- Maintain existing colors
- Suggest new 'family café' handwritten font
- Provide separate file of little chef head

Ideal skills and experience:
- Proficiency in vector graphic design
- Experience with logo design and font selection
- Familiarity with handwritten font styles